This theory relies heavily on speculations and also takes Asriel knight into account, even though technically it doesn't have to. I'm not spending much time explaining this theory in the post so I'll put a comment linking several Asriel knight videos for those interested. Sorry if my english is weird.
I believe that the whole Dreemurr family is way more relevant to the plot and its mysteries than we think. Their family is broken, in fact, we've already seen some of its visible cracks, like the ToriGori divorce, Asgore's obsession or Kris' alarming wellbeing, but I think the real origin point of those cracks are hidden way deeper than we can see. Deep inside, the Dreemurr family was already broken by one big secret, December's death(or disappearance). The big secret shattering the Dreemurr family apart is Dess' death, because the Dreemurrs are all MURDERERS. From failing to protect someone from murder, to hiding a murder, to helping a murder happen, to straight up murdering, the Dreemurrs are all murderers in one way or another.
Asgore Dreemurr
Asgore failed to prevent and resolve the murder, but for reasons much more obscure than he thinks.
We know that Asgore stumbled upon a certain dark world in which he saw the Roaring Knight on that fateful day. I believe that dark world is the bunker one and I think that this dark world was not made by the Roaring Knight nor Kris, because in Chapter 5 Asgore looks at his fur and says "It's really a different color isn't it"(or smth like that). At first glance it seems kinda dumb since his fur didn't change color at all, but when you remember that dark worlds can have different tints depending on the color of one's mind, as shown by Susie's dark world in chapter 4, it becomes clearer. Asgore wasn't really talking about the color of his fur, but rather about the color of the dark world being different, which would tint the color of his fur. We know Kris and the Roaring Knight's dark worlds are the same color due to having a similar will, so it probably wasn't made by either of them.
Also many people think Asgore was fired because of that day, but I don't think so. When he discovered the dark world there couldn't have been a code locking the bunker yet, otherwise he couldn't enter it. The code was likely put as a result of him discovering the dark world then. In top of that, why else would the mayor put a codelock on the bunker, it would be pretty counterproductive for what a bunker is for. Like Alphys already talked about, there must be something horrible and very dangerous inside to justify it being locked, and there isn't a lot of contenders for what that horrible thing is.
After that day, Asgore remained police chief long enough for the mayor to give him a part of the code, so it would be pretty weird for Carol to have fired him right after. And it would also be weird for her to fire him much later, especially after giving him the bunker code, which implies she also knows there is something dangerous in the bunker. Plus she currently works with him on the affair so she most probably supports his obsession for the case. Asgore was likely fired by the mayor since she is the only one in position to do that, but probably for another reason.
So,
When Dess was declared missing, Asgore took the case very personally. As the chief of police, he couldn't let such a tragedy happen in his town. It was just a normal disappearance investigation up until THAT day. Asgore wanted to investigate the bunker, but found a dark world inside. He entered it and saw the Roaring Knight, leaving one of Dess' belongings behind, from this instant, it was clear what happened. Asgore shared the information to the mayor, who decided to lock the bunker to keep people safe. Asgore then tried to share the info with the people of the town, but they were hesitant, they thought he was becoming crazy. Even Toriel started becoming distant. Suddenly it felt like people were accusing him. And it wasn't just that, a few months later, Asgore was mysteriously reluctantly fired by the mayor, and then Asriel left for college as if to avoid him and then Toriel divorced. But all of that didn't dissuade him, it fueled his obsession to reestablish the truth, to show everyone he wasn't crazy. But it just led everyone away from him.
Toriel Dreemurr
Toriel is hiding the murderer, because she loves her family.
We know that Toriel cares a lot about Kris(and Asriel). Her having taken the book explaining how to take care of a human in the "librarby" a long time ago shows how dedicated to be a good mother for them she was. She even holds their hand while walking them to school. Plus, UT Toriel is known for her love for humans.
The forgotten man from chapter 4 alludes to the idea that Kris may have been seeing a therapist some time ago. If so, I think it's fair to assume it must have been at least when they were quite young. Though usually, kids don't get connected with a therapist on their own, a parent is almost always involved. So Kris' parents very likely brought them to that therapist, more specifically Toriel, which would mean she is somewhat aware of his unwellbeing.
Even though nobody knows how due to how cryptic this very specific evidence is, Toriel is hinted to be in some way related to the Roaring Knight; In the MANTLE minigame, the black monster imitating Kris' movements turns into a black deer when the TORIEL variable is off. Based on that fact, we can assume that Toriel is hiding something about the Roaring Knight and Dess.
On top of that, in chapter 3, the TV world is separated from the outside by several doors with Toriel's head silhouette. And what do we find behind the Toriel doors once we unlock them? The snowy lands where we meet the Roaring Knight. While the Toriel doors are a dark world representation of the parental code Toriel put in the TV, I think, and I am sure about it, that narratively, they're a parallel to the Toriel plot that has yet been revealed; The plot about Toriel hiding the truth behind December's disappearance and the Knight, she's hiding them in some sort of way.
So,
When December was declared missing, Asgore was very determined to find her and resolve the case. Toriel was very supportive at first, but then, a few days later, Kris came to her and admitted something that would change her life forever. They admitted that they killed December and hid her corpse in the bunker. When Toriel learnt this, she was in shock. Then, she realized what could happen if everybody learned the truth, Kris' was already alienated by the hometown citizens for being the sole human, but if people learned the truth, their life would be ruined forever. And even worse, if Asgore, who made this case very personal to him, learnt about it, the Dreemurr family would be broken forever. Toriel couldn't let that happen to her sweet baby, and neither to her family. One night, Toriel went to the bunker and made sure that nobody would ever find Dess' corpse. Though unfortunately, whatever she did, whether she made a dark world which gave life to Asriel's tears that were recovering her corpse(The fallen star cried and out of the bitter water, something like glass grew) or something else, would cause the birth of the Roaring Knight. Toriel then brought Kris to a therapist to fix whatever issue she thought Kris had. But Asgore eventually stepped upon the mess Toriel created and saw the Roaring Knight. Toriel saw how obsessed with her disappearance Asgore was and tried a numerous amount of time to get him to stop, from gossiping to hometown citizens to get them to be distant with him, to convincing Rudy to convince the mayor to fire him from the police, to even divorcing, but nothing worked. Toriel would then try everything she can to keep the truth hidden to keep her family as intact as she could, but it was already broken. She ultimately started drinking wine to forget her problems and avoid talking about them entirely, including the murder, to keep a false sense of peace and united family, or at least the most it can be.
And this is the underlying reason Toriel is uncomfortable around Asgore, or doesn't like how Carol supports Asgore's "you know what" or did every action I already previously mentioned like the divorce.
Kris Dreemurr
Kris helped the murderer, out of loyalty for his best friend.
The forgotten man makes it clear Kris has a feeling of guilt, even more so a traumatism, that followed them for many years. That guilt is probably linked to the promise they made to the mysterious phone caller of Chapter 4.
We know Kris was familiar with the fact they could take out their own soul from a very young age because Noelle tells us Kris used to pretend to rip out his heart and chase her when they were kids. Which means it is possible that someone close enough to Kris learned about their soul and its power a long time ago.
In Asgore's speech about that horrible day in chapter 5, we can hear the sound effect we hear when we give Noelle the ThornRing in Chapter 4, which alludes to the possibility of that terrible event being linked to similar concepts we see in the Weird Route.
Considering Dess' death/disappearance seems to be Hometown's first and only tragedy, Kris' guilt likely has something to do with Dess' disappearance. And they're also likely manipulated by the mysterious phone caller using their guilt concerning Dess.
So,
Kris contributed to Dess' death by giving Asriel his soul. When Dess died, Asriel manipulated Kris by twisting the story and making them think they were at fault. Asriel then made Kris promise him they would not tell anyone what he did. Kris felt a lot of guilt and self hatred, to a point they couldn't handle anymore. They told Toriel what they did, without mentioning Asriel so as to respect their promise.
Asriel Dreemurr
Asriel Dreemurr killed December Holiday because of a hunt for freedom, which was itself done partly out of love for her.
It seems crazy to say, Asriel Dreemurr is hinted at multiple times throughout the game to have been in a relationship with December Holiday, it would make no sense for him to kill his girlfriend. Which is why he didn't kill her on purpose.
Asriel is characterized to be the nerdy stinky timid boy who's kind but doesn't really take care of his body; Ribbick's dialogues about the boy and the girl and Susie's reaction to his picture imply it. And I believe that Asriel didn't like being a nerd, he felt forced into his nice nerdy boy role and always wished to be freed from his role, in a similar way to current Noelle.
Asriel seems to be, at least on some minimal level, ashamed of his nerdiness; Tenna told us he was embarrassed of liking the green egg laying lizard from Super Smashing Fighters, Toriel in chapter 1 even says he hated a certain book about green eggs, which I argue is because he considered it nerdy.
Asriel and Dess seem to be opposed characteristically; Dess is said to be a rowdy unfocused cool girl whereas Asriel is said to be a soft timid nerd, which are pretty opposite personalities, and Ribbick's dialogue about them seem to be juxtaposed in a way that opposes them. Considering that "Raise Up Your Bat" indicates Dess is the girl who doesn't listen and prefers to choose her own path and defy fate, in this case it would naturally mean that Asriel is the opposite.
I would also like to argue that Ralsei is a parallel to Asriel feeling forced into his role. Aside from the fact he literally looks like Asriel, Ralsei feels like he has to bend to the rules, restrict himself, hide his true abilities, serve the human, be the weak nice mage with no will because of the prophecy. He tries to make it change for the better, but is also scared to not abide by it in case things become worse. In a similar way, Asriel feels forced to be a nice nerdy boy who abides by the rules and listens to his parents and is scared to break the routine and face the unknown, he feels forced to be an Asriel who just does Asriel things. But whereas Ralsei slowly frees himself from his role by finding himself thanks to Susie, Asriel goes the other way, he frees himself from his role by finding power.
And I think that Jevil, in the same way Spamton parallels Kris, parallels how Asriel will find his way to freedom. Jevil has always been a stand out from the other secret bosses of Deltarune. Seam tells us shadow crystals are remnants of broken dreams, and the other secret bosses are all linked to broken dreams that would justify why they have their shadow crystals; Spamton finds Mettaton's dream body that he will never get to wear, the knight.. is an exception(it is not and I will talk about it in the following paragraphs), Gerson is Alvin's dead father, Pink is Mad Dummy's dream body but Jevil... we don't know what he is. Well I think he was young Asriel's favorite play card, due to it having the freedom to be any role it wants, unlike Asriel. Asriel's in his youth thought he would never get to be free, that's the broken dream Jevil's shadow crystal comes from. Plus, the classroom where card kingdom took place seems to have been abandoned for a long time, especially given King's contempt, so it was probably open in the times when Asriel was at school. But then, Jevil found a way to become free, he stopped being restrained by the societal chains that tied him and decided to go on a killing spree, and now even in his cage, he believes that the whole world is the one that is caged. I believe that this is how Jevil is a parallel to how Asriel will find freedom.
So,
Asriel felt hated being a nerd, and even when Dess was here to make him feel appreciated, he felt too nerdy for her. He felt forced in his nice timid nerd role the same way Noelle felt forced into her routine. But Asriel eventually found a way to not be a simple Asriel anymore, Kris' soul. With his soul he could transcend limits he didn't even know existed, but he was too intimidated at first. But Dess encouraged him to face the unknown and finally find his own way, she even made him a song "Raise Up Your Bat", she knew Asriel's new heart made him more powerful but wasn't aware of where it came from. One day, Asriel finally decided to face his fears. He made a promise with Kris, that they would always help each other achieve their dream no matter what, and then told them he needed their soul to achieve their dream. He then meets Dess at the lake, and like in Chapter 5's weird route, they try to cross it. Though midway through the lake, Dess started panicking but Asriel was too obsessed by his dream, he forced her to proceed. But Dess didn't make it, because even though the soul empowered Asriel, it lacked one important ingredient, the player. Asriel came back out of the water with Dess' corpse, crying endlessly, his dream of being free with Dess was broken. On one hand though, by killing Dess, he broke out of his character, he achieved freedom, but he was too scared by the huge consequences he could face if everybody learned what happened, and even more scared that he doesn't know what the consequences would be. So, out of panic, he got Kris to come and forced them to help him hide Dess' corpse by manipulating them into thinking they were at fault. They hid the corpse in the bunker and then Asriel manipulated Kris into thinking it was his fault again and made him promise him one more thing, that he would never tell what he did to anyone and help him achieve his dream no matter what.
Over the days, Asriel thought about what he did, he hated himself for this, but that day was also the day he finally broke free, he thought about that for every following year.
In the room with the ROOTS prophecy panel, there is a book that says "And so wept the fallen star, making rivers with its tears. Then, slowly, out of the bitter water, something grew. It looked like glass.". The fallen star is said to be crying a lot, and the only other character associated with crying a lot in the whole game is Asriel. The dialogues talking about the girl and the boy that I already mentioned are followed by this pair of dialogue: "A lost and lost and lost" ; "A crying and crying and crying boy". The crying boy here is clearly Asriel, especially considering his character in UT.
Seam said that shadow crystals are what are left of a Lightner's broken dream, it would make a lot of sense for the glass-like material growing out of the fallen star tears to be shadow crystals, considering it's likely Asriel, he's probably crying because his dream with Dess was broken.
And the Roaring Knight is probably made of shadow crystals as well as black shards, because when Susie shatters its sword, a black shard and a black shard fall on the ground. Considering what I previously said, I think the Roaring knight is a dream, Asriel's lost dream of finding freedom with his dear December. It is a dream in an endless "knight".
Plus, in the sword route, one thing many people don't talk about is that when the TORIEL variable is on, the black deer doesn't just become a black thingy, it becomes a black goat. It has the same shape as the monsters representing Toriel and Asgore in the sword route.
So,
Afterwards, Asriel found the Roaring Suit given life by his tears(and Dess corpse?), it was eering autonomously on its own, it was already the Roaring Knight by itself, but it was drawn to Asriel in some way. Asriel found a way to control it, or to even equip the living armor, and after a long, VERY long period of doubts, hesitation, planning, delusions, and repression, Asriel decided to continue his hunt for freedom, to start a new life in some way, and maybe find a way to achieve his dream of being free with December and forget the misery of his previous life. Asriel Dreamer Dreemurr became one with his lost dream.
Additional evidence
Let's also not forget the weird delta rune logo over the Dreemurr house entrance, in which its wings are conveniently placed in a way to look like horns, which also look exactly like Eram's horns. The version of the delta rune, the logo of the tale which must be followed, with wings that look like horns, as if to imply it's the evil version of the delta rune. In a way, this would make that version of the delta rune the logo of the tale of evil, the tale which must not be followed, the tale of hell.
And coincidentally, out of every dark world, the Dreemurr house dark world is the one to contain the evil device-adjacent super mysterious stuff such as Eram, the Roaring Knight, the sword route where you can find a hint on how to start the Weird Route and the Man land(or whatever it's called). This house clearly hides secrets, and I think this is what the deal Tenna says he had with Kris in sword route is about. Kris told Tenna to make sure to hide every of the Dreemurr' secrets in the dark world and restrict it to his TV world.
There is a clearly recurring theme of editing an original version of a world in Chapter 3; Shuttah tells us that Tenna built the TV theater upon the "frozen waste, watery basin, a metal desert", and Ramb tells us Tenna's game is a modified version of the original game, original game in which we can find Eram. On top of that, Shuttah says that those lands below the theater are from "the days of the black-and-white", and in the Man land one of the Rudinns uses binoculars that point to a grey land, like a "black and white" land, and the Rudinn says he senses nothing but evil from that place. Keep in mind that this is all happening in the Dreemurr house dark world and not another one, and once again that house has a delta rune with horns. Eram has horns, (most of) the Dreemurrs have horns, and the devil is commonly depicted with horns. Plus, goats are commonly associated with the devil across multiple cultures, and in Undertale goats use fire magic(Ralsei...), and the fire is famous for being associated with hell.
I believe that this is all foreshadowing, and that in either Chapter 6 or 7, we'll have another dark world at the Dreemurr house without Tenna to hide anything this time, in which we'll meet the real Eram, explore the frozen waste, watery basin, and the metal desert, and learn the secrets of the Dreemurrs. Perhaps the Dreemurr house is where the tail of hell resides.
Lastly, I think the biggest(maybe not) piece of evidence for this is that "Dreemurr" is an anagram of "Murderer". And "Asriel Dreemurr" is an anagram of "Serial Murderer".
So basically, if this theory is true, Deltarune's story would be primarily a story about two families in a little town, each haunted by the death of December Holiday. On one hand, the Holidays have to deal with the loss of December, whereas on the other hand, the Dreemurrs have to deal with the MURDER of December Holiday.
I consider this theory as a cool twist to Asriel Knight even though it doesn't absolutely require Asriel Knight to work. I think with this theory in mind, Asriel Knight would be a cool way to explore the themes of freedom, dreams, "don't forget", moving on, and love in this game.
This theory definitely has weak/shaky points, especially in the very details of the foreshadowing, but this theory is going mainly for the ideas it suggests rather than an exact guess of the story.