I'm probably wrong: But I'm assuming that by the time the hard cap is reached, enough people will be on the network to sustain the blockchain without the miners. At the moment, it's mainly the miners keep it going (they're on 24/7, after all) - but once the currency reaches a critical mass, the miners aren't strictly neccesary any more - their only real role is to bring value into the economy and sustain a healthy level on inflation...
As I said, I'm probably wrong