That doesn't make the program incorrect, it just means that you can't provide that particular input to the program.
That is not good. It's hard to reason about such a program, in other words can you trust results of such a program? How do you know whether your input caused Ub at some point or not?
The burden of sanitizing the input is on the user (either programmer or the data provider).
Checking this is usually a performance tradeoff, so it was decided not to be done by default.