It depends on the situation, if the time that the last Bitcoin gets mined and it is widely used as a currency (not as investment) and reached its mass adoption,  Bitcoin price will surely be more stabilized but the biggest challenge that Bitcoin will be facing at that time is, will it still be profitable for miners by just relying on transaction fees since there is no more rewards for every block they will mine. If not, for sure miners will switch to other cryptocurrency but I think that there are still miners that will remain (small time miners).