How semi-cooperative games handle players who have nothing to lose?
The social contract does most of the heavy lifting

The social contract is an unspoken agreement between all the players of the game as to how the game should be played to maximize the enjoyment of all the players.  (Sometimes it's a spoken agreement, especially in tabletop roleplaying games.  Regardless, it's always present.)

The goal of a game isn't to win.  The goal is to have an enjoyable play experience.  That's why Cards Against Humanity is a much more popular game than Rock-Paper-Scissors, even though your odds of winning are lower.  

Of course, winning generally contributes to the experience of a game.  For some people, in some games, it contributes a great deal.  But in other games, victory takes a back seat to the process of the game itself.

Semi-cooperative games are almost exclusively highly thematic, highly variable games.  These are not the sorts of games that attract players whose primary method of enjoying games is to 'win'.  Instead these games are designed to reward players who enjoy creating a narrative together, who want to do things just to see what will happen, and have a good story to tell at the end.

This means that players are less likely to feel dissatisfied because they aren't winning as much as one of the other players, and are still incentive to avoid the big loss conditions.

Also, even if a player does decide to tank the whole thing out of frustration, that doesn't necessarily mean a negative play experience for everyone else.  There's a reason that LEEROOY JENKINS! became the battlecry of the internet for a while.  Dramatic disaster can be just as fun as dramatic victory.

Which is not to say that a discontented player can't ruin the experience for other players.  The mechanical structures that Volker talks about are built in to reinforce it against this sort of behavior, and they're there for a reason.  But the bulk of the heavy lifting is done social contract, by making the focus of the game be about something other than victory.