A system that has effectively bifurcated with conflicting chain tips caused by rewriting history with new nodes unable to tell which is original, or a fully centralized stake-mining where a subset of stake voters game the system to unfairly select themselves out of proportion of their stake weight.
A proof-of-work fork is an unstable situation, resolved when more work is applied to one side vs the other, which inevitably happens without active intervention. A proof-of-stake fork is permanent--someone new to the network has no built-in mechanism for deciding which side to prefer: they both seem equally valid.
A properly constructed proof-of-work mechanism has no built-in mechanism for a malicious minority hash power to take control of the protocol, shutting out the higher hash rate majority from mining blocks.
