Most bugs aren't going to create any risk for data exfiltration. In most real application servers (which are very rarely written in C or C++ these days), requests are almost completely isolated from each other except to the extent that they interact with a database. If you detect a bug in one request, you just abort the one request, and there's likely no way it could affect others.
This is part of why something like Rust is usable at all; in the real world a lot of logic has straightforward, linear lifecycles. To the extent that it doesn't, you can push the long-lived state into something like an external database, and now your application has straightforward lifecycles again where the goal of a task is to produce commands to manipulate the database and then exit.
Except you usually can because the state isn't completely unknown. You might not expect some field in a structure to be null, but you still know for example that there's no way for one request to have a reference to another, so you just abort the one request and continue.
