Miners collect transaction fees too.
It is also worth to add that it will be very slow process. Not like miners are getting reward poof miners are not getting reward. Reward will decrease each 4 years until it will reach little more than 1 sat (after more than 100 years from now). After another 4 years and next halving reward will be smaller than 1 sat - not transferable - no reward other than fees.
I don't think that anyone will even notice this 1 sat but if it will be imporant for miners i don't see a reason why not soft fork BTC adding micro-satoshi (1/1000 of 1 satoshi) and continue to reward miners for another 40 years thanks to extra 3 decimals.
It is not possible to run out of coins. Even If 99% of supply is burned (lost wallets etc), price exploded and currency is not tradable (price is to high to pay for small things) you can always add decimals just like during hyperinflation elites are cutting decimals to avoid carrying money in a wheelbarrow instead of a wallet.