Maybe in some cases but my father died on the 2nd day of the month and his SS check usually arrived on the 3rd day of the month. The Post Office in his town returned the envelope marked Deceased.
They may be required to do so if they are aware of a death.
Your father’s SS check was for the month previous so he was due that check. When a person gets the check it is a month behind. Only if it was the next month would the post office have been in the right to send it back and I;’m not sure even then. They have to deliver any letters until it is told not to.