If I don't use all my tuiton assistance during the year. Does the remainder carry over to the next year? Or does the government take it back?

Having gone through the tuition assistance program for all my degrees I can sadly say that once the year rolls over whatever portion of your TA that you didn't use is gone. However, once the year rolls it bumps back up to the original amount.

You use it or lose it. It has no cash value for you so they are not taking anything back, they are just not paying it out. But you can still use the benefits the next year if you are eligible.

use it or lose it