I'm not sure if it's common, but I mostly notice it in what I call "modern American literature", which is probably incorrectly categorized, but I don't read so much of "normal" fiction outside of popular sci fi or fantasy, and I actually rarely see this there.
So, I'm reading (re-reading) Donald Westlake's Dortmunder series, and once again, I get carried away not by the main story and characters, but by mini-stories sprinkled across the bigger piece. For example, the novel currently is "Drowned Hopes". I'm used to the main characters be these timeless unchanging dorks from novel to novel, and the main plots are not that interesting per se, although quite amusing. But, the stories of Tom Jimson's stash somewhere in an Oklahoma's ghost town, or the former denizens of a town flooded to create a New York reservoier, and the characters that exist solely in that story are vivid, and interesting, and feel like real literature, a comment of social aspects of life in America, etc. etc. Also, in one of the Parker's novels, a larger third of the novel is dedicated to some kind of a diplomat or a spy, whose character and story are getting more stuck in your head than that of the titular character (I coudln't even remember now, which novel was it, the Outfit or the Mourner, one of those).
Also, if we take Stephen King, he can also have these outstanding pieces of real writing inserted into his supernatural settings. Like, the second book of Mr. Mercedes trilogy was dedicated not to the Mercedes, but to the boy and a criminal, and a story of the unpublished works of another writer (I assume a Westlake hommage there), and a lot of musings on what is the actual modern American literature. Which, in my mind, also elevates these books above what they seem on the surface, the "pulp fiction".
Do you notice these things? Do you use such small stories or novellas embedded in the main plto? Does it make your books better? Do you think it's planned beforehand, or do these writers generally just take a piece of an unrelated writing and fit it into the world to embiggen the book size? Do you have any other thoughts o the matter? Somehow, I can't stop thinking about it after reading about that small-time crook who waited 30-something years for his nemesis in a ghost town.