Tenured professors can be fired for a variety of reasons, the most common being incompetence, negligence, immoral/personal conduct, and financial exigency.
Several questions:
- Do these four reasons also apply to firing endowed professors? I'm guessing financial exigency does not apply because the endowment covers the costs. The other three I am not sure about, since presumably the endowed professor doesn't have formal responsibilities (again since the endowment removes the need to teach/supervise/etc).
- Between the donor, the department, and the university, which of the three sets the rules? For example, can the donor say "we require our endowed professor to do good research, and are opposed to termination for any reason as long as he/she is doing good research"? (I note King George V felt something similar about the Victoria Cross)
- If the endowed professor can be and is fired, does the search for the next professor start immediately, following the standard process? I'm guessing yes since I don't see any reason why not.