Two things might happen:
1. People might finally start using the satoshi and mini Satoshi for good due to increasing price
2. People might move on to other cryptocurrencies since they believe bitcoins have reached his full potential, it would essentially mean the developers can try and push the limit of the highest number of bitcoins that can be mined.
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I do believe that bitcoins will continue to increase in price due to demand and supply. People who are holding bitcoins since the beginning would actually be benefited. It would be a positive phenomenon for the long term holders.
We have to wait till the year 2140 to see what would actually happen.
But before all this there would be adjustments needed in the code to make sure everything works perfectly. Since in the year 2106 it would be dead if the already known bug is not fixed.
Of course, we will not live until 2140, but even if this happens earlier or there are very few bitcoins, there is no reason for miners and bitcoin owners to worry, I think the situation for them, on the contrary, will improve.