Sometimes grad students change advisers. In some cases this is a brilliant move, saving the student's sanity and academic career, and in some cases this is one more step on the road to flaming out of graduate school(s).
I considered moving to another university partway through my graduate school days. My adviser was OK, but another professor who was on my committee was tormenting me, and I saw no reason why I should continue to put up with that for many more years. There were other reasons as well, all of which added up to motivation to move somewhere else, even if it meant losing time and effort. Then the evil professor died (he was ancient and had been quite ill) and I decided to stay where I was.
As a professor and adviser, I have taken on grad students who have had unsuccessful experiences with other advisers, and I have had a few of my own students switch to another adviser. In most of the cases involving intra-departmental moves, these adviser changes have not had good results for the students or for the advisers. In fact, the students who have switched from working with me to working with another adviser in the same department have ended up failing/quitting, and the one student I adopted from another adviser (at my previous university) also flamed out, after moving on to a third adviser. When I wrote about this topic before, however, commenters told stories of some successful switches to more compatible advisers.
The cases that tend not to work out are when students are looking for an easier adviser (i.e., one with lower expectations) or the students are not feeling motivated by a particular research topic and hope that by changing advisers they will find the motivation they are seeking.
More successful switches involve talented and motivated students who are seeking a better fit for their interests and abilities or who are leaving an unacceptable situation for an adviser who may be more sane.
Every once in a while I see a graduate application involving a student who wants to leave their current university and who indicate, either directly or by omission, that they do no want their adviser to be asked for a letter of recommendation. What to do? Call the adviser anyway (especially if it is someone you know) but keep in mind that you may not be getting a complete story, or just go by the student's record in the application?
In one case in which I was involved, I did not ask the adviser for an opinion but another professor at the other university made a very strong case for the student. This other professor was concerned that the student's application would be undermined by the lack of a letter from the adviser and wanted to make it clear that the student wasn't the problem, the adviser was the problem. The student was accepted, came to work in my department as one of my advisees, and did very well. He lost some time but said it was worth it.
I'm not sure what would have happened without that information from the other professor, but it certainly helped to get a strong positive recommendation. I think it is important that faculty do such things for students if they feel that the students are talented and would do well if given another chance with another adviser. It would also be a good idea for students to seek out such sympathetic faculty and request that the issue of student-adviser incompatibility by addressed proactively and directly in a reference letter or phone call.
Switching advisers is a difficult thing to do. Sometimes it is the best thing to do, but it should only be done if absolutely necessary, given the costs in terms of time, effort, and stress.
8 months ago