It depends on the laws under which the company (or other organization) is constituted. In most cases the shareholders of a company can hold a meeting to elect

It depends on the laws under which the company (or other organization) is constituted. In most cases the shareholders of a company can hold a meeting to elect new directors; in the case of a society without shareholders, the society membership would be able to elect directors. For a society with no members, the society would simply be dissolved -- typically that only happens if a society is insolvent and the members leave rather than being stuck with the debts.