Sometimes you'd like to visit all elements of some logical array in a random order, with each element pointing to the next, e.g., to benchmark the speed of pointer chasing. Using Sattolo, you can set up such a full-sized linked list fairly simply, e.g.:
I have used it a half dozen times in more or less that specific context.
Random ordering of elements in a list is often used in maze generation. It's possible that a permutation that had only one cycle might produce a maze with a particular structure.