If at any time during the period of assistance the recipient thereof becomes possessed of any property or income in excess of the amount stated in the application provided for in § 2304 of this title, the recipient shall immediately notify the Commission of the receipt or possession of such property or income and the Commission may, after investigation, either cancel the assistance or alter the amount thereof in accordance with the circumstances. Any assistance paid after the recipient has come into possession of such property or income and in excess of the recipient's need shall be recoverable by the Commission as a debt due it. Such action for the recovery of assistance shall not be abated by the death of the recipient.