With Ethereum's algorithm I don't think this is the case (without some serious changes) because if you can prove that an address staked on a different chain then you can penalize that address on the main chain. I guess ultimately as long as you make sure that you empty out the address on the main chain, the main chain will simply disregard your attempts to claim a stake as being without merit. I don't know that anyone has analyzed the general case of an ongoing fork; the entire point of a proof-of-X is to be able to definitely prove from scratch that a given fork is the "correct" one simply by examining all alternative forks presented.
What happens in case of a hard fork like the ETH/ETC fork? (Assuming something similar happens in the future after the PoS has been released.) Can you move the proof from a chain to the other across hard forks?
During the ETH/ETC fork replay attacks were terrible until people figured out how to make a contract that was guaranteed to act differently in the two chains; you would send your ETH to that address, providing two output addresses, and your ETH would go to one and your ETC would go to the other.
Before that was commonplace there were numerous problems of transactions being replayed causing all sorts of problems.
If someone wanted to fork post-PoS ETH, chances are they would have to do so very deliberately, with code on the new fork deliberately designed to prevent replay attacks, as was done in the BTC/BCH fork.
