I guess the real question here is how will the miners survive the after all of the supply is mined. They might get something out of the fees but I think there is another way that they can survive after this, they may leave Bitcoin and start mining other crypto currencies but still, I don't know about that, I'm just guessing. All I know is that Bitcoin may change after that, I mean maybe.
As of now, the average fee per block amounts to somewhere between
BTC0.50 and
BTC2.0, with the median being approx.
BTC1.00. The current block reward is
BTC12.50 per block, which will decline to
BTC6.25 by 2020. By 2032, the block reward will be
BTC0.78125, which is less than the average fee per block (at current levels). By 2060, the block reward will be reduced to less than
BTC0.006. So we don't need to look to the distant future to check whether miners will survive or not. Within the next one or two decades, it will become clear whether they are able to survive on the transaction fees or not.