Or even much sooner, when there's only 2 or 10 left to mine?
I guess because by that point the price of electricity to mine will become so huge no one will want to, and the psychological deterrent of buying insanely expensive coins. I can see it crashing because people will think "well there's no more supply, and those that have it won't relinquish it." I don't know there's an economic term for it, something like fatigue.
Firstly, mining difficulty is not static: Ranchiogo discussed about it in an above post. It is adjusted with a specific time to reflect the current level of the hash rate. There's no instant clarity where everyone realizes that only few coins are left to be mined and the cost of mining shoots up.
Also, if all Bitcoin's are mined it doesn't mean there's no more supply. Close to $19 million bitcoins has been mined out of the total supply, and that would be way higher before the next halving, meaning the bulk of coins are already in circulation now and those that have it do relinquish it, billions of dollars in transaction volume are completed regularly using Bitcoin.