Without any legal appointment, nobody automatically has a right to manage your assets or make decisions on your behalf. Not even your husband or wife.
Your loved one would have to apply to a Tribunal in order to be appointed your financial manager or Guardian. If the Tribunal believes that person to be not fit for the task, then it may appoint a governmental body, the NSW Trustee and Guardian, to manage your affairs.
This can be a long and stressful process, especially at a time when your loss of capacity would likely be causing stress and difficulty in itself. Galluzzo Lawyers strongly recommends you sort your affairs out in advance.