You sign and add "signed in protest." A boss from one of my college jobs was dealing with shady ass individuals wielding power plays all the time. They did everything they could to get him to quit. Didn't happen and they never had grounds to fire him. Basically everything they did was more fuel for a lawsuit that he could've filed.
It seems to be a common thing where fuck offs get to keep their job and the ones who are committed and do a good job lose theirs. I've worked for more than one company where the boss liked to employ simpletons. Mostly, and this is purely my theory, because the boss is a know nothing asstard who has to surround themselves with people equally as ignorant, if not more, so they look smarter. These hires are also yes men. If you need your ego stroked you hire yes men.