You can appoint an agent prior to your death under this law as well. Most places give you three days off in the event of the death of an IMMEDIATE family member; mother, father ,sister or brother.If the company has surviving shareholders, they can call a general meeting and pass a resolution to appoint a new director. When a sole director dies – and if there are surviving shareholders or members – they can hold a shareholders' meeting to appoint a new director. The beneficiary is then free to call meetings and appoint a director of their choosing. Form DIR-12: In respect of director who has been appointed in the office of vacating director within 30 days of such appointment. In most cases the remaining directors can continue running the company and simply share out the deceased officer's responsibilities.