I LOVE this concept! Like an 'endangered species' or legendary valuable (almost of mythical status, perhaps, if it's truly the last coin ever made).
If I were playing this game, I would have to add in museums as a strong faction contender (I could see them vying all over the world to get it), billionaire collectors, religious zealots (who all claim currency began with them), etc. Everyone wants its power!
But it would end with a simple hole in the pocket, as so many coins do... ;)