Earlier quoted context omitted.
What's a frequently encountered case for such cyclic loops? Without details I'm drawn to trying to break the cycle, either by promoting the shared state to a container object for the set, or by breaking it out into it's own object that multiple things can point at.
a parent field. a doubly linked list
Parent field is something where you have a clear hierarchy (it's not really “cyclic”, so it's the perfect use-case for weak references).
When coming from a managed-memory language, this obviously requires some conceptual effort to understand why this is a problem at all and how to deal with it, but when compared to C or C++, the situation is much better in Rust.