In theory, there are some attacks in POS chains that would make the malicious chain indistinguishable from the honest chain, therefore they need check-points. But the problem - how do you decentralize check-pointing. And for those projects that claim they have, they are hard to analyze.
Yeah, there seems to be no way to do this algorithmically, i.e. with pure PoS.
So the system in principle relies on the fact that people, not computers, are able to collectively remember some sort of checkpoints (albeit with the help of computers/servers). And it of course also relies on the fact that stakers/stakeholders won't risk the punishment associated with trying an attack.
In some POS blockchains/networks, there's check-pointing that's signed by a centralized entity - usually the developers - every X blocks to ensure that that is the real history to be followed.
To find out is simple - Attack Bitcoin. If the attackers are successful with that, then Bitcoin has no right to exist.
Ha, that's pretty cold.

If an attacker/attackers could be successful in getting more than 51% of the Hashing Power behind him/her/them, AND overcome the network's army of full nodes, then that would prove that Bitcoin has failed and therefore it has no reason to exist.