Interesting and reasonable question.

First, you can mine at http://coin-base.net/infinite

As far as what happens now, well, you are right, we are asymptotically approaching 0, but that is by design.  The reward halves each time.  So, we knew it was happening.

The coins are out there, and will continue to trade and be used.  The supply will just stop growing... and the hope is that the demand increases.

My $.02

First, you can mine at http://coin-base.net/infinite

That URL is 404... I cannot find an IFC mining pool that is operating right now.

I am glad to see there is some activity in this forum;

I did not realize that transfer fees were redistributed to the coin network to the miners; thanks