On the whole, I’d have to say I’m not a big fan of stories embedded inside of stories. I haven’t seen very many of them done very well, not that I’m an expert or have read everything on the planet that might contain one or two examples. I’ve often found it ‘cheapens’ the reading experience for a reader as though the author didn’t have anything to say really during that particular scene but needed something to take up space. If so, I can do that and maybe I should try my hand at it sometime.
This goes for those embedded stories that actually have something to do with the original story surrounding it too. Surely, one or two exists somewhere; I’m currently reading an anthology of horror and fantasy that contains one or two of these kinds of works and they’ve won awards (none from me in case you might wonder), but maybe that’s why writers do just that–to fill space with stuff that can’t really be presented any other way without boring the reader to tears or making a reader wonder, “How the heck did the character know all that?”
(BTW, that last part was a fine example of a run-on sentence, don't you think?)