Is a university responsible for its graduate students' education?

I have heard some stories lately about graduate students getting pretty much “dropped” by their universities when their academic advisers leave for one reason or another. Graduate students seem to depend on their advisers more than undergrads, so if a student’s adviser were to leave their university, it would be a lot more difficult for a grad student to continue their studies.

For example, I know a woman who has been studying for her PhD for three years. Now, her adviser has left and no other faculty members seem to want to take her in. At this point, she may either have to find an adviser at a different university entirely, or she will effectively be kicked out of the school, thus wasting three years of money and effort.

Do universities have an obligation to their grad students to make sure they complete their studies, as long as they pass the proper exams and such? Should a university make sure that when an academic adviser leaves, another will be there to take their place? Or is a graduate student more or less on their own to complete their education in these circumstances?

Maybe this phenomenon is specific to this particular university, but I’ve heard it happens all the time. I would like to know people’s opinions on this topic.