Rust memory management is just RAII, and there are no exceptions, just nice Result types and syntax that makes returning them and handling error cases simple and pleasant.
If you want to handle closing a socket, it’s as easy as implementing the Drop trait on your type. Without an unsafe block there’s no way your destructor won’t be called.
struct Socket(u16);
impl Drop for Socket {...}
To answer your question there’s no special casing around memory vs non-memory resources. Your socket is backed by a kernel ID which must exist in memory, of course, so by adding a Drop implementation you can then define the special treatment yourself. If threading considerations exist you can explore the Sync and Send marker traits too.
It’s largely a much simpler language than C++, you just have to learn how to write it. A lot of the friction/confusion IMO is that it looks so similar to languages you use at first glance you just start writing the code you used to in a Rust-y way, instead of Rust, then are frustrated as to why it won’t build.
In some ways it’d be clearer if it looked “foreign” like prolog — it’d be a lot less popular though haha.