Bitcoin design already addresses this issue and contains necessary mechanisms to make bitcoin sustainable even after block rewards get stopped.
Block miner will receive transaction fees, and when it is economically not rewarding for the labor/cost out there, some miners naturally will stop mining. However, since Bitcoin network difficulty adjustment will take care of average block length to be 10 minutes, thus network difficulty will drop and mining cost will drop. Eventually, mining cost will be less than mining reward that can be collected from transactions fees. So, bitcoin protocol has the necessary adaptation capability to handle your concerned case. No worry