PROB §6611: (a) Subject to the limitations and conditions specified in this section, the person or persons in whom title vested pursuant to Section 6609 are personally liable for the unsecured debts of the decede

(a) Subject to the limitations and conditions specified in this section, the person or persons in whom title vested pursuant to Section 6609 are personally liable for the unsecured debts of the decedent. (b) The personal liability of a person under this section does not exceed the fair market value at the date of the decedent’s death of the property title to which vested in that person pursuant to Section 6609, less the total of all of the following: (1) The amount of any liens and encumbrances on that property. (2) The value of any probate homestead interest set apart under Section 6520 out of that property. (3) The value of any other property set aside under Section 6510 out of that property. (c) In any action or proceeding based upon an unsecured debt of the decedent, the surviving spouse of the decedent, the child or children of the decedent, or the guardian of the minor child or children of the decedent, may assert any defense, cross-complaint, or setoff which would have been available to the decedent if the decedent had not died. (d) If proceedings are commenced in this state for the administration of the estate of the decedent and the time for filing claims has commenced, any action upon the personal liability of a person under this section is barred to the same extent as provided for claims under Part 4 (commencing with Section 9000) of Division 7, except as to the following: (1) Creditors who commence judicial proceedings for the enforcement of the debt and serve the person liable under this section with the complaint therein prior to the expiration of the time for filing claims. (2) Creditors who have or who secure an acknowledgment in writing of the person liable under this section that that person is liable for the debts. (3) Creditors who file a timely claim in the proceedings for the administration of the estate of the decedent. (e) Section 366.2 of the Code of Civil Procedure applies in an action under this section.