A trust assumption of PoS (Proof of Stake) is that >66% of the stake is honest. If you violate this trust assumption then yes PoS breaks. This is a similar trust assumption to requiring that 51% of the mining power in PoW (Proof of Work) is not malicious.
This risk can be mitigated:
1. The network should halt if a fork is detected. A fork with more than 66% of the stake behaving maliciously means a fundamental trust assumption of the network has been violated. Stop everything! Let humans figure out what is going on. I'm not saying every PoS system WILL halt under these circumstances, but as a countermeasure they SHOULD be designed to halt and value safety over partition resilience. Thus, an attacker forking a PoS must never allow parties to see either side of the fork. If a party notices a fork occurs, they will halt and can't be double spent against.
2. Following from 1, how do you prevent parties from communicating and discovering that a fork is occurring? Are you a tier-1 ISP and can control all internet traffic? You can defend against such attacks by making it very hard to hide the presence of a fork via redundant communication mechanisms. For instance the Bitcoin blockchain is broadcasted via satellite, a PoS blockchain could do that as well.
3. Additionally you can require that stakers lock their stake for long periods of time e.g., 6 months. This means that if an attacker wants to perform this attack and truly have nothing at stake they must cause a fork in the chain before the 6-months ago mark. Parties who are up to date with the latest chain are not vulnerable since they have already accepted the consensus history of chain. New parties who are syncing for the first time would be vulnerable, however clients could be programmed to have hardcoded 6th month checkpoints or clients could check block explorers and halt if a fork is detected.
