Each person who is designated as a successor of the decedent in a certified copy of an affidavit issued under Section 13202 is personally liable to the extent provided in Section 13207 for the unsecured debts of the decedent. Any such debt may be enforced against the person in the same manner as it could have been enforced against the decedent if the decedent had not died. In any action based upon the debt, the person may assert any defense, cross-complaint, or setoff that would have been available to the decedent if the decedent had not died. Nothing in this section permits enforcement of a claim that is barred under Part 4 (commencing with Section 9000) of Division 7. Section 366.2 of the Code of Civil Procedure applies in an action under this section.