What scope is shared in between function executions in a Deployed TSv2 function

This is a follow up to my previous question on shared scopes: Are static class properties shared across concurrent function invocations in Foundry Functions?

In the official docs, Deploy functions, there is this line:

The long-lived nature of deployed functions means that local caching may be possible if the function is tolerant to restarts.

Are there any more details on this? It sounds like even in deployed mode, each function still executes in its own sandbox? but maybe there is some sort of global scope that is maintained between executions for a single function/sandbox?

How do I read/write from this local cache? When (if at all) does it go out of scope/get cleared out?