you can always assume that someone will be mining
Eventually, mining stops, since the supply of potential coins is capped at a number about 4x the current number in existence.
That isn't how is works. Even without the reward, miners will be doing it for the transaction fees. All transaction have to be stuck in a block, even after the reward is gone. The miners will no longer be mining for a pre-set reward, but for the transaction fees of the transaction in the block they make. Even now they get that reward, but it is usually pretty small compared to the 50 BTC reward. Although I have seen at least one block with 3 BTC of fees in it.
The upshot is that mining must continue as long as bitcoin lives.