The Facility (2006)

From the introduction The Facility is a game for 2-4 players. One player will be the GM and the others will take on the role of reincarnating souls. ... The Facility offers souls the chance to reincarnate in bodies that they provide. Each player plays one of these reincarnated souls. The "catch" is that the bodies you reincarnate into only live for one day. You can get a new body, but each time you reincarnate you get a little weaker. Eventually souls suffer from Burn Out and can not be reincarnated again.