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.