I don't understand how a bore snake can become stuck? If you can't continue to pull it through for any reason (such as the thin cord breaking or becoming detached from the thicker "snake" part), why not just pull it back out the way it went in? At no point in using a bore snake is the whole of it inside the barrel. There's always a decent amount poking out one end or the other to get hold of, even without the thin pull cord.
