I think it depends on the job the program is being used for. If the program is used in a setting where occasional crash has no severe consequences, say search engine backend, it may be useful for the company to actually run in production a program that is allowed to crash whenever severe error condition occurs. In scenarios where lives or lots of money hinge on program being alive and functioning, such as plane autopilot, or rocket / space probe control, crash or fatal error of the main program often means disaster and thus should never occur. If error condition occurs during execution, the program should withstand that and continue with default path of execution. In the past lots of lives and money could be saved if only the software and hardware conformed to this paradigm.
I agree with 'it depends' except for the case of safety critical systems, which I actually have experience in. A proper safety critical system should also be able to withstand a crash in an arbitrary process. The thing to remember is that there is no default path of execution if there is undefined behavior in C or C++ code. The process may do the worst thing it can, at least with the OS-level permissions it has.
