Hi Joybelle48,
s201F of the Corporations Act 2001 provides that, in the event of the death of a single member/director of a proprietary company, the executor appointed to administer the deceased’s estate may appoint a new director to the company. The director has all the powers, rights and duties of the deceased director and can keep the company running until shares are transferred to beneficiaries who may then appoint new directors if they wish. As far as I know she could appoint herself as director of this company.