If a nonprofit board has only one staff, the exec and it just plain doesn't like its Exec (not about competency but personality) does it have the ok to just exercise it's authority and fire that Exec, without cause and or consequence?
Of course the answer is: it depends. Yes, the board can fire "at will". No, it may not escape consequence. For instance, firing without cause may open the board up for suit by that exec -- wrongful cause for instance but this is speculative because really, anyone can sue anyone for just about anything -- they may not win but they certainly can sue.
What may really be "consequence" relates more to funders' response; staff's response, and client's response. Each will respond if not react and each can make it difficult for the board to now move-on for the benefit of the organization. Funders in particular could conceivably have the biggest reaction and more importantly could even challenge the board for its action, particularly if it only hears of the change.
Boards be ware, actions like firing your exec require special planning and extra communication to make the transition one that is smooth.