All guardian/conservatorships are terminated on death, but some may be able to be "restored" and deemed by the court to be a whole person once again. Immediately they gain all of their rights and are responsible for their finances.
Restoration is done by a ward showing progress in an environment that is less and less restrictive. They will eventually be able to live independently, while still being a ward of the Public Administrator.
They will also need to take initiative during this process. This initiative takes the form of independently performing regular tasks, such as:
Assisting in the process of transitioning into independence