The is the essence of the "nothing-at-stake" problem with PoS that, despite claims to the contrary, remains unsolved (and IMO very likely unsolvable).
I believe it might be solvable. Satoshi relies on the idea of the majority of people being "honest miners" for the system to function. A reputation system can be used to solve some of these problems since it is nothing more than a ledger of "honest miners". I'm not really a fan of Invictus or NXT, but both systems seem to be moving towards experimenting with that solution.