claiming tokens only applies to ICO buyers. they have to "claim" them to bring them into existence. once they exist, then they exist. they have no claim to them if they sell them on an exchange afterwards.
when the native EOS platform launches you need to have an ethereum address associated with an EOS address, or you won't get your tokens. if you have this done by snapshot next year then any EOS held in that Eth address will get snapshotted to the native EOS platform.
so once you own the token it's yours, your concern should be in getting prepared for the snapshot next year because it says outright on the EOS website, "we're hoping that noobies will fuck up and not map their Eth address to an EOS address for the snapshot, reducing the total EOS supply and making ours more valuable," with instructions on how to do this hidden away in a section labelled "advanced participation" so that anybody not confident enough to fuck with things labelled "advanced" will completely skip it.
i like this project alot but that kind of bothers me.