Mark Dominus writes about a notional "Journal of the Empty Set", which would publish papers on results about mathematical objects that don't actually exist. He asks: "But on the other hand, suppose you had been granted a doctorate on the strength of your thesis on the properties of objects from some class which was subsequently shown to be empty. Wouldn't you feel at least a bit like a fraud?"
There's a (perhaps apocryphal) story that's made the rounds in my department about one possible way to fail your thesis defense. Namely, it's said that a student went to their defense and began by defining the sort of group they were studying. There was a rather long list of conditions, and one of the examiners quickly proved there was no such group. The student therefore failed.
The good thing about combinatorics? That sort of thing doesn't happen. Usually we can actually construct explicit examples of the things we're talking about.