With relatively few exceptions, if your program hits undefined behavior, then your program was already doing something pretty wrong to begin with. Signed overflow is a poignant example: in how many contexts is INT_MAX + 1 overflowing to INT_MIN actually sane semantics? Unless you're immediately attempting to check the result to see if it overflowed (which is extremely rare in the code I see), this overflow is almost certain to be unexpected, and a program which would have permitted this was not "previously fine" nor "meticulously written."
I feel compelled right now to point out that software development is a field where it is routine to tell users that it's their fault for expecting our products to work (that's what the big all-caps block of every software license and EULA says, translated into simple English).