I am not aware of a genre or subgenre but a work that consists of parts that can be read on their own (and that is not simply a short-story collection) tends to rely on a frame narrative or frame story. However, not all works that employ this literary technique consist of parts that can be read in isolation. Below are a few examples of works containing stories that can be read on their own:
- The Decameron by Giovanni Boccaccio (14th century),
- The Canterbury Tales by Geoffrey Chaucer (late 15th century),
- One Thousand and One Nights (many authors; Middle Ages),
- Heptaméron by Marguerite de Navarre (first half of the 16th century),
- Unterhaltungen deutscher Ausgewanderten by Johann Wolfgang Goethe (late 18th century),
- Manuscrit trouvé à Saragosse by Jan Potocki (late 18th - early 19th century).
However, some works use a frame story but the "stories" within that frame don't make much sense when read outside of their context. In many cases, the "inner story" is a single continuing story. Examples include the following:
- The Odyssey (c.8th century BC) (part of it is Odysseus telling what has happened to him),
- Frankenstein; or, The Modern Prometheus by Mary Shelley (early 19th century),
- Wuthering Heights by Emily Brontë (1840s),
- If on a winter's night a traveler by Italo Calvino (1970s): each of the "even" chapters is the first chapter of a book.
I am not aware of a term that refers the first type of works without including the second type.
If there is a term for the sort of genre or style described in the question, I would expect this to be mentioned in entries for "frame story" or related terms in glossaries of literary terms. However, I couldn't find any references to such a genre or style in the entries for "frame story" in the Concise Oxford Dictionary of Literary Terms by Chris Baldick (second edition, 2001), The Penguin Dictionary of Literary Terms and Literary Theory by J. A. Cuddon (third edition, 1992) or the Algemeen letterkundig lexicon (online, in Dutch).
L. Kip Wheeler's online glossary of literary terms mentions the term pericope for the embedded stories, but this seems to be a term from biblical studies. None of the reference works have an entry for "pericope".