I tried Rust about five years ago and I had trouble expressing cyclic data structures because there is no clear "owner" in a cyclic data structure. The "safe" solution recommended by the rustaceans was to use integers as references to the data in a vec or hashmap. I was rather put off by this: Instead of juggling pointers I was juggling integers. It made the code harder to debug and find logic errors. At least when I…
Seriously, just use unsafe. “Welp, can’t write a doubly-linked list in safe Rust so I might as well use C” is throwing the baby, the bathtub, and the rest of the greater metro area out with the bathwater.
I would have used inheritance to create a "ListBaseType" with a "ListElementType" specialization (with all the data required to wrap some element) and an empty "ListNullType" to use as begin/end elements. A quick Google search results in a implementation using "None" instead: https://gist.github.com/matey-jack/3e19b6370c6f7036a9119b79a... (I don't vouch for it!)
In the end the correctness boils down to correctly handling the beginning/end. It does matter little if that's a NULL, None, nullptr or ListNullType.
The real difficulty would be adding thread safety with minimal performance loss.