Nope. Memory safety means no undefined behaviour. Crashing is defined behaviour. Indeed, at least in the D philosophy it is better to crash than to just do something and continue when a bug is detected. If that were not the case, assertions in released code would be total humbug.

Now, detecting such errors statically at compile time is still valuable where it is practical. But it's common knowledge that no language guarantees no bugs. It follows that a complete "no crashing" guarantee is not even desirable, let alone part of a memory safety guarantee.

Having the program exit when a memory safety fault is detected is entirely safe.

What about bounds checking on array access, like most memory safe languages?