The naming of an executor in a will shall not operate to extinguish any claim which the deceased had against him, but it shall be the duty of every such executor accepting the trust to give in such claim in the list of debts. On his failure to give in such claim or any part thereof, any person interested in the estate may allege the facts by petition to the court, and the court shall decide on the validity of the claim, if it be denied. When the claim is established, the executor shall account for it as a debtor to the estate, and not otherwise; and in the same way and subject to all the foregoing provisions, an administrator shall give in a claim against himself.