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.
Don't expect us to live in the future, we cannot tell exactly what will happen by then but analysis from what we have presently tells us that surviving on transaction fees will be possible, new miners are going to evolve and some older miners will also have to drop because they can't match the cost of running a mine, but it is certain that miners are going to exist because our transaction fees will be worth a reasonable amount as reward to existing miners.