If the server decides to escalate the issue to the programmer, e.g. by invoking the debugger, then yes, it would most likely hang until the programmer interactively resolves the problem (e.g. by issuing a proper restart), and only then execution would proceed.

However, that doesn't need to be the case; it is still possible to e.g. do the industry standard, which is to log all available information about the request and program state to some sort of log file or crash dumps, return a HTTP 500, and start waiting for another request. The possibility of interactive resolution of exceptional situations is a possibility, not a requirement.

It's also possible to block and invoke the debugger only in some cases, e.g. when some global debug variable is set to true. In all other cases, the system can behave automatically.