Actually there is a game wich has that kind of ending. It is called Shadow Hunter. In the beginning people get a random card (hidden for the other players) with a character on it and a win condition associated. There are three factions : Shadows : They have to "kill" all the Hunters Hunters : They have to "kill" all the Shadows Neutral : Each one has a particular goal.
- Shadows : They have to "kill" all the Hunters
- Hunters : They have to "kill" all the Shadows
- Neutral : Each one has a particular goal.
If there are enough players in the game, there are characters from the three factions in play. And if a Neutral makes it to the end of the game but has not fulfilled it's win condition, then it's a non-winning player.
This is not really what you described as not all the players begin with the same win/loose conditions. But because it is random everybody begins with the same odds of having a win/loose character (shadow or hunter) or having a win/loose/nothing character.
I hope my answer is useful to you.