(a) Regardless of whether the statute of limitations otherwise applicable to a claim will expire before or after the following times, a claim rejected in whole or in part is barred as to the part rejected unless, within the following times, the creditor commences an action on the claim or the matter is referred to a referee or to arbitration:
(1) If the claim is due at the time the notice of rejection is given, 90 days after the notice is given.
(2) If the claim is not due at the time the notice of rejection is given, 90 days after the claim becomes due.
(b) The time during which there is a vacancy in the office of the personal representative shall be excluded from the period determined under subdivision (a).