The board is in absolute control in a not-for-profit. The loophole is that some have bylaws that make ad-hoc board meetings and management change votes very difficult to call for non-operating board members, and it can take months to get a motion to fire the CEO up for a vote.
In some not-for-profits, the board often even manages to recruit and seat new board members. Some not-for-profits operate as membership associations, where the organization’s membership elects the board members to terms.
On the few not-for-profits where I was a board member, we started every meeting with a motion to retain the Executive Director (CEO). If the vote failed, so did the Executive Director.