I don't think that will be happening anytime soon, but if that happened, no one would be buying your bitcoins and even purse.io wouldn't accept BTC. I can't predict how bitcoin is reaching a situation where it can't be traded for USD and fiat.
It's very simple, if one option is not working anymore, then there is always an alternative way to get what you are looking for. It would mean that peer-to-peer trading will be even more important. Services as localbitcoins will see an explosive growth.