Final answer:
In a non-fiduciary board, the responsibility that can never be removed is the duty of loyalty.
Step-by-step explanation:
In a non-fiduciary board every member of the board has a duty to act in the best interests of the organization they serve. One responsibility that can never be removed from a non-fiduciary board is the duty of loyalty. The duty of loyalty requires board members to always act in the best interests of the organization, avoid conflicts of interest, and put the organization's interests above their own.
For example, if a board member has a personal financial interest in a decision being made by the board, they are obligated to disclose that interest and either recuse themselves from the decision-making process or handle the conflict of interest appropriately.