The title is a bit of a trick question, because of the way the bitcoin block reward gets smaller is asymptotically, meaning it gets close to zero but never touches. However it will get small enough and close enough to zero where if the price wont be able to support miners anymore so they will have to rely almost entirely on transaction fees.
This idea is a big part of why many miners wanted to increase the block size rather than work on second level solutions, primarily because if things go the way of level two solutions, transaction fees will be much smaller. If people use the lightning network and have 10 transactions, most likely they will only actually settle on chain a single time. When you have invested hundreds of millions into the mining business, you have to work towards a future that keeps you relevant.
The big problem many people are afraid of is if the profit isn’t there for miners to continue to secure the network. More likely than not mining will become sort of a utility where people are making at cost or very miniscule amounts of money providing hashpower. Just like today, those who have the cheapest electricity are really going to be the only ones who can compete, but companies might run miners at a cost just to support the network as well. Also as the technology and mining chips get smaller, they also tend to use up less electricity so we might see miners that are very cheap to run.
Right now miners have a oligopoly on mining equipment, but as time goes on that wont be the case Once you hit the smallest nanometer tech available today, you wont have to worry about your miner being replaced in a year and you can make large investments. Also mining companies might simply pivot to those selling the shovels instead of mining the gold just out of necessity. In a perfect world this is the case, because if miners have too much power, users end up getting hurt.
So when we get to a level where almost all the coins have been mined and mining must rely on transactions fees to survive, I suspect we will see a big shift in who actually runs the mining hardware and what kind of services are being offered. It wont happen all at once, every block halving we will start to see these changes take place.
Thanks to @Elyaque for the badges