Earlier quoted context omitted.
I was once in a presentation for a math PhD thesis. During the thesis, the evaluator of the thesis noticed a flaw in their proof. The student understood and then asked “What now?” The evaluator prof simply shrugged.
That sounds like the worst "exam nightmare" scenario imaginable, but did the student get the PhD in the end?
Mistakes in proofs are relatively common, but such a mistake doesn't automatically mean that the proof is entirely wrong. Many times, the mistake is just in the exposition, and can be fixed easily. Other times, the mistake is fixable and the fix is apparent. Perhaps the author forget to treat a relatively trivial edge case. In the first two cases, the student would likely just pass with minor corrections to be submitted soon.
Sometimes, of course, the proof is just wrong. That is the dangerous case, which will cause either major corrections or failure.