When checks come back to you, AP should hold the checks! Such checks are prime opportunities for fraud. If AP were to send to those who requested the refund to the patient, who know the patient is not looking for these refunds, they could easily keep and cash them.
First, though, AP should verify that they entered the address correctly into the AP system. If you did, then send a request (but not the check) to the requestor to check their records and research to get a proper address. (It is usually protocol for all patients to give a copy of their driver’s license. That should be the best address.)
To control the open check, it should be monitored and guarded by AP. If all records lead to the incorrect address, AP needs to comply with the escheat law of the state of the last known address.