One potential probate client question:  If a payer (an executor under a will, or a trustee of a trust) overpays a beneficiary when a family member dies, does the payer have a right to ask for the money back?

Absolutely!  You do not have a right to keep funds given by mistake. Consult a local probate attorney regarding the statute of limitations on recovery of the disbursement.  If the beneficiary refuses to return the balance, the executor will sue on behalf of the trust, and the costs of suit might be added to the recovery.