If the miners shut down,because the fees are unprofitable,the hashrate/mining difficulty will get adjusted,which means that mining will become easier,which means that it will become profitable again.
On the other hand,most of the miners are hoarding Bitcoins,which means that they are expecting more ATH prices in the future,which means that even if BTC mining isn't profitable all the time,a future BTC price above 100K USD might make it extremely profitable.
Even if BTC mining is unprofitable for a long period of time,many miners could switch of altcoin mining,by choosing altcoins that have profitable mining.
This is why it is rarely ever unprofitable to mine, if it ever becomes unprofitable then people stop and difficulty drop and it becomes profitable yet again. It is a system that arranges itself and makes sure that people profit.
It would be very hard for it to be unprofitable though, considering how much transaction fees are spent every single day. We need to realize that the volume is huge on bitcoin, this may not work for some other coins which doesn't have this kind of transaction fees or volume but it definitely works amazingly for bitcoin. As long as people end up using bitcoin then they will spend fees and that will be more than enough for sure.