Texas Estates Code - EST § 355.202. Claims Against Personal Representatives

(a) The naming of an executor in a will does not extinguish a just claim that the decedent had against the person named as executor.

(b) If a personal representative is indebted to the decedent, the representative shall account for the debt in the same manner as if the debt were cash in the representative's possession.

(c) Notwithstanding Subsection (b), a personal representative is required to account for the debt only from the date the debt becomes due if the debt was not due at the time the representative received letters testamentary or of administration.