That is incorrect, after slightly less than 21 million have been created, blocks will stop having a reward.
Ok, but these blocks will still be assigned to people. What if people start trading them as a separate currency? You see what I mean...
There are quite a few problems with that. First of all how do you transfer ownership of a block? I very highly doubt blocks will ever be traded (if you can even figure out a way to do that).
Oh, I get it. The first transaction in the block assigns a number of bitcoins to an address that is chosen by the creator of the block. The software is currently configured to reject blocks that assign an incorrect number. That is a number that is not according to the sequence: 50, 25, 12,5, etc for respectively 4 years each. So you say, that at some point in time the block creator cannot add an extra transaction assigning bitcoins to himself anymore?