When someone dies who controls a permanent but does not own it, what happens?
You get your permanent back. 


  800.4. Unlike two-player games, multiplayer games can continue after one or more players have left the game.
  
  800.4a. When a player leaves the game, all objects (see rule 109) owned by that player leave the game, any effects which give that
  player control of any objects or players end, and all spells and
  abilities controlled by that player on the stack cease to exist. Then,
  if there are any objects still controlled by that player, those
  objects are exiled. This is not a state-based action. It happens as
  soon as the player leaves the game. If the player who left the game
  had priority at the time he or she left, priority passes to the next
  player in turn order who’s still in the game.


Check out this related question for some more info: In Magic free-for-all multiplayer, what happens when someone dies?