If your list is laid-out a contiguously in memory as structs with both next and prev ptrs, you can visit each member using ptr arith and switch the values without actually walking the list using next and prev. Ditto if there's an underlying data-structure involved such as an array.
You allocate an array of objects that contain pointers, then link them together. It does not have all of the typical benefits of a linked list (in particular, there's a hard max size and may require a fixed size, depending on just what you're doing to it here) but it does allow O(1) reordering elements for a list-order traversal, while also allowing a linear traversal through memory.
If the linked list has a loop, but you don't know it, how do you figure out the length of the list to allocate enough space for your array? How do you copy the list into the array without traversing the list? How do you traverse the list without hitting the loop and looping infinitely?
If you know that all the elements in the loop are already in the array then traversing it is easy. Of course, if you have an upper bound for the length of the list, there's an easier check...