Joseph: Sorry, by cases I thought you meant actual cases, not Halachos. Yes, there are Dinim brought down about what happens in specific potential situations, but there is no case brought down where it happens. Also, you are misunderstanding the Mishna in Nedarim.
I agree that divorces aren’t granted just because someone asks for it. I just think that you made up your claim that there are many cases in Gemara and Shulchan Aruch where what you claim happens.