Okay, I got that. However, calling it a problem is a rather bold claim. I would call it a property of PoS.
It is more than a "property" it is an as of yet unresolved problem. There is no security in PoS unless it is resolved.
(No matter if PoS or PoW)
Um, well no. I can't mine using computing power I no longer have (but did have at one point in the past).
How would want to be on that fork anyway? In doing so, they would destroy every single bit of confidence in that very cryptocurrency.
The cost to the attacker is absolutely zero. If he can gain anything more than zero he has everything to gain and nothing to lose. It would destroy confidence in the PoS currency you are correct especially when it happens over and over and over without end. That is why it is the Pos problem.