Lets not assume everyone stops mining, but lets say the largest miners who have dedicated warehouses full of miners stop mining. This would cause the network to come to a screeching halt, no blocks would be found until the block difficulty readjusts. This happens every 2 weeks. Bitcoins mining algorithm is about guessing random numbers, and hoping you get lucky. The mining difficulty indicates the threshold of a valid magic number. Any number less than the given difficulty is a valid block. Any number larger than the given difficulty is considered an invalid block by Bitcoins mining algorithm.
If all large miners were to stop mining, the mining difficulty would decrease (the magic number that determines block validity would actually increase), which means miners can now find a number larger than when large miners were mining and have the block be valid.