What happens to the Meister when they complete a Death Scythe?
In the anime, Maka's mom is referenced many times by Maka, who says that she occasionally gets postcards from places her mother has been to. Therefore, I'm assuming that after a Meister makes a Death Scythe, they take on a job like any other person would, or maybe some special mission from Lord Death himself. After all, after the Weapons become Scythes, they go around the world protecting different parts of the world.

This is just a theory. The answer may have been revealed in the manga, but I don't know for certain. I hope this helped a little bit.