It depends. In my case, there is only one prof doing what I do in my school (my advisor), so the answer would be a clear no. In contrast, a friend was doing a

It depends. In my case, there is only one prof doing what I do in my school (my advisor), so the answer would be a clear no. In contrast, a friend was doing a more broad topic and after some strong disagreements, was able to switch mid-race. Another friend was finishing his PhD at a top econ school, and his mother died so he flew back and took a couple of months off. Even though he already had job offers and a completed paper, his advisor (a well known asshole in the field) was so pissed off that he stopped all form of comunication, and my friend had to switch advisors and start a new paper because no one else did that specific topic in the school. So yes. Luck matters a lot, and YMMV. Your advisor could die, get a nobel prize, or just have a bad day, and it would change things drastically for you.