Well, it's not totally clear to me what the question is asking for, but in medicine and related fields, where this kind of def is encountered more often, it's called a definition by exclusion or, --more commonly-- a diagnosis of exclusion. There are several such examples in the linked articles: dyslexia etc. E.g. one such def is/was that:
A person is ‘dyslexic’ if no alternative explanation can be offered for their reading and writing difficulties.
It basically entails following some flowchart of classification and if all/other "known" explanatory/nosological grouping(s) fail to apply, the one given "by exclusion" [of the others] is then the default one. The UFO example seems to fit this pretty well, as it entails first trying to explain some observation by other means, and failing that, applying the "unidentified flying object" label.
Less commonly the same term (of definition by exclusion) has been applied to police powers, at least in some of its former conceptions. But this is a somewhat broader use in the sense that it relies on vagueness just as much as it does on exclusion.