the funding could come from scholarship, fellowship, assistantship (research, teaching, project) or others. for graduate assistantship there is no guarantee whatsoever, it's really just like having a job and keeping it for the rest of your study. if you lost your job, you lost your support, and you will have to pay tuition.
it's true that most graduate students don't pay tuition, but i know people who are Masters and Ph.D. students and had a couple months/a semester lapse in their assistantship so they had to pay tuition from their own pocket.