If uo keep them on your wallet, and the chain splits, x coins would result in x coins in one chain and x coins in the other.
If you keep them at a "bitcoin bank", the bank may refuse to give you the coins on one of the chains, something like this happened when ethereum split (some "wallets" refused to give users their ETC).
Keep them on a paper wallet, and then, if you think it is wise, trade them after the dust settles.
Interesting, I wasn't aware that this occurred. I'd like to read more about it, can you share a site or reference details on when this happened and with which ethereum "Bank".
Remember that all of these Bitcoin bank companies have a lot to lose if they f*ck with customer accounts. They're all making decent money providing the services they offer, and all of it is built on trust. If they violate that trust, they go out of business...that's a pretty severe consequence.