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.

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.