Bitcoin Miners will 'live' on the transaction fees - no more new coins 'minted' as part of the block reward.

Keep in mind, these Bitcoin miners can go elsewhere and there are plenty of somewhat self interested people/projects coming up with alternatives and forks to Bitcoin.

Most of these projects are of questionable value. There was Bitcoin Cash developed in response to high transaction fees and Bitcoin Gold is trying to be ASIC resistant - which means it wants to be good for mining on regular Graphic Processing Units.

Some coins don't have a cap. Ethereum for example currently has no upper limit, although it is likely to change in the future to be a Proof of Stake instead of Proof of Work (mining) coin.

Hope that helps, happy to go over any of this in more detail.