Not so, it's considered a player's own personal property:It has happened in Survivor USA twice that I know of, once the thief went thru someones bag and took the idol, and once when the thief followed the idol holder to where he buried it, and dug it up, and yes if you can steal it, its yours, in USA.
https://www.realityblurred.com/realitytv/2012/10/survivor-one-world-idol-stealing/