Many players do. A jury is formed of the last several voted off; they vote for which of the final two or three players deserves the million dollar prize. And in its two seasons in 2011, the show changed its formula to include Redemption Island, for the first time allowing people to possibly return to the game after being voted off at Tribal Council (the whole iconic "the tribe has spoken"/ snuff their torch that represents life/ "time for you to go" thing). Last season Ozzy, already a strong personality who'd played before, used Redemption Island to his advantage, focusing on his health and diet while by himself and away from the politics and personality clashes of the rest of the show.
There could be other ways to get players involved even after they're gone.
What if someone voted off at the contest's halfway point was invited to stay and have the same access to information on the contest that host/producer Jeff Probst has? And stick around and comment on what was going on with those still playing? Maybe that player could just show up every once in a while at camp, walk through, say "Hey guys, remember me?" and leave without explaining further, leaving them to go "Wait: why isn't s/he gone? What's s/he doing here? What's going on?" Probst can be good at being unreadable -- though when he's surprised, which still happens sometimes (including this season), that's a thing of beauty -- but having a more readable, thought-to-be-gone player be there, to surprise players and to give them some other factor to think and worry about as they navigate the game, could be a devious, delicious complication.
What if that re-visiting player even got to consult with the producers? Be in on decisions like when to merge multiple tribes into one, or what rewards they'd play for, or whether they'd have to, say, move to a new camp site? And let the players know that someone they'd gotten rid of was -- or could be -- affecting the game? That player should probably forfeit being on the jury, but that player's potential effect on the game behind-the-scenes could be even bigger.
Could it be Survivor: The Variable? Or, more deviously, could it be Survivor: Puppet Master? You couldn't call it Survivor: The Mole or Survivor: The X-Factor; those names have been taken. And Survivor: Mua Ha Ha Haaaa! would just be mean.
I'm a Survivor fan. And good at unworkable ideas.