Undefined behaviour is undefined only by the standard - an implementation may choose to handle undefined behaviour in some documented, specific fashion. Undefined behaviour exists to give implementations exactly this flexibility.

> an implementation may choose to handle undefined behaviour in some documented, specific fashion

Or they can leave it undefined and not make any guarantees. I do not think that any compilers on any platform makes any guarantee on signed overflow.

true, but the behavior of unsigned integers is defined such that they can't overflow. the "wrapping" behavior of unsigned ints is defined: you get the arithmetic result modulo the max value for that width.