I can see it crashing because people will think "well there's no more supply, and those that have it won't relinquish it."
First, you are confusing
supply with
production. They are completely different things.
The idea that people won't "relinquish" their bitcoins is not reasonable. People sell now when the price is rising. Why wouldn't they sell in the future? Besides, your bitcoins are worth nothing if you never let go of them.
Regardless, prices rise when supply falls assuming demand remains constant.