(a) A personal representative may not allow a claim for money against a decedent or the decedent's estate if a suit on the claim is barred:
(1) under Section 355.060, 355.064, or 355.201(b); or
(2) by an applicable general statute of limitation.
(b) A claim for money that is allowed by the personal representative shall be disapproved if the court is satisfied that the claim is barred, including because the limitation has run.