California Code, Probate Code - PROB § 858

If a proceeding has been brought under this part by a conservator on behalf of a conservatee, or by a guardian on behalf of a minor, and the conservatee or minor dies during the pendency of the proceeding, the personal representative of the conservatee or minor's estate or other successor in interest may proceed with the matter and the existing proceeding shall not be dismissed on account of the death of the conservatee or minor.