My language (Lily) handles the problem by trying to avoid the gc where it can.
Lily is statically-typed, built-in classes can't be inherited from, and there's no C-like casting.
With those rules in mind, most objects can't become cyclical. It's impossible for a list of strings to loop back onto itself, for example. It helps that the value classes backing enums (like Option and Either) are immutable, which I so far suspect prevents a cycle.
That at least allows you to group classes into three groups:
These never cycle (Integer)
These may cycle (List)
These always cycle (Dynamic, linked lists?)