If it suddenly stops, it will be difficult to sustain mining on transaction fees alone. This would certainly put security at risk and the future of bitcoin would be uncertain. But only time will tell whether it can survive. I don't think that will happen at all. But if it does, the market would be completely destroyed.
Transaction fee will be enough for miners if all bitcoin are mined. Transaction fee will be high in the year 2140 because bitcoin will also be very expensive at that time. Bitcoin network cannot stop because if any miner is not interested anymore due to lack of incentive will pack his bag and leave. Other miners will keep the network going.
For now it's enough for miners but the more Bitcoin hash rate becomes difficult, more and more sophisticated machines are roll out to miners and this matchines are very expensive. Back then, anyone with their PC could mine Bitcoin which was cheap, with time s9 miners were rollout as the difficulty increases ordinary PC couldn't keep up and people switch to that but again, it's now too difficult to do solo mining unless you joined a pool which makes rewards smaller and work harder.
Unless the cost of producing blocks reduce, mining is going to be difficult by that time but developers are not worried right now because:
-Bitcoin price is increasing which means more money for miners to cover expenses.
-we are still very far from when mining rewards will be too insignificant, many years ahead that many of us might not be alive till then.
For that I believe, they will provide a concensus solution when the time is right about this block reward.