Earlier in this thread I mentioned that there is nothing said about the fate of Saruman's Ring, so it is possible he took it into the Shire with him. When he was killed I would imagine the ring was picked up by the Hobbits, maybe to languish in a Mathom House?
Or did Sam pick it up?
If it had any kind of property that helped in Saruman's Orc breeding programme, was it an influence on Sam's own personal Hobbit breeding programme?