Usefulness of a linked list with a cycle Is a singly-linked list that contains a cycle considered a corrupted data structure or is there some practical use for it?

(You could argue that a car without its front shield is not corrupted, if the owner intends for it to be like that, so lets understand the word "corrupted" in a sense of "damaged into state that it is useless".)

One of the possible ideas that I got is that it can represent some sort of a computation: the initial "non-cycled head" of the list can be viewed as the initialisation phase, whereas the "cycled tail" can serve as a never-ending computation. However, this reasoning is a bit Texas Sharp-shooter fallacy to me.

Any ideas?
In the case of circular linked list - this might be a buffer, neat structure to handle operations that must be consecutive or form a ring (like in parallel programming).

What if not the whole list is cycle?
This might be intended like conflict resolving, and thanks to cycle it will not go further.
It might be the case that every operation changes state so there is cycle, but it will eventually resolve.  

If you write a turn-based game with general loop, there might be cycle if user can do something multiple times per turn. So here it is intended.

And totally not constructive - cycle came from bug, so it pushes application into infinite computation.