I encountered a program where the stipend every year comes from TAing/RAing (no more than 20hrs a week), unless you are on a fellowship. If you are on a fellowship, then the stipend/teaching money rolls over to the next semester or year. So, it seems that with that program it'd be in your best interest to be continually applying to fellowships, which I guess could be a good or bad thing. On the one hand it is slightly more work, on the other it's evidence of an ability to find money within the university and outside of the university.
To be fair, the department does actively give you fellowships as well. They are just not guaranteed every year. So if a semester comes and they have not given you a fellowship or you have not secured one on your own, then you will be TAing or RAing.
As for my last question, I meant does the money for that year or semester just disappear? But it's been answered. I think the general result is that money rolls over.