> A safe section of code that panics unexpectedly might preserve memory safety invariants but hork the higher-level logical invariants of your application

The usual way of dealing with this is to use impl Drop to cleanup properly. Resources are guaranteed to be dropped as expected on panic unwinds. Eg the database transaction rolls back if dropped without committing.

> Imagine an attacker who can force a panic in a network service, aborting his request but not killing the server, such that the panic on his next request grants him some kind of access he shouldn't have had due to the panic leaving the program in a bad state.

You need to be more specific. Why would the web server be left in a bad state because of such panics (in safe rust). All the memory will be cleaned up, all the database transactions will be cleaned up, mutexes might get poisoned, but that's considered a bug and it'll just cause another panic the next time someone tries to lock the mutex.