Putting aside the obvious “not if there is a clear and agreed upon plan for naming their replacements,” there is actually a very different last resort for organizations (typically non-profits) that are deemed to be in service of the community (even if just as a place of employment but especially when they are furthering a mission) where the courts are granted custody of the non-profit and appoint a respected member of the community to maintain core operations as they oversee the process of creating a new board of directors, possibly by setting up elections, creating a committee to establish new governing bylaws, etc so that the good a non-profit has been doing isn’t wholly undone by the dissolution of its governing body.