It depends on the program. One thing to consider is that your funding support could be (and almost certainly will be) tied to your advisor, so changing to a bet

It depends on the program. One thing to consider is that your funding support could be (and almost certainly will be) tied to your advisor, so changing to a better advisor will probably have financial implications. This sort of thing is exactly the kind of thing that prospective PhD students should ask programs about before signing up, by the way. Don't be afraid to ask lots and lots of questions about things like funding, what qualifying exams are like, what happens to people who don't pass quals, whether anybody's ever changed advisors, what happens if an advisor's funding dries up, etc. etc. As somebody who's interviewed prospective PhD students, I like hearing those kinds of questions, even when I don't have good answers to them- it shows that the prospective student is doing their homework.