I recently moved. I have not changed my address on my Amazon seller account, and I have sent my packages to customers. However, it looks like some of my packages will be returned, as they show “Package was refused” or “Incorrect Address” if the customer does not receive the package and USPS/FedEx/UPS tries to deliver to my old business address.
In my experience, nothing else happens. They’ll just deliver it to your old address since that’s what’s on the label. If they don’t accept it (which hardly ever happens), it’ll end up at the local Post Office or go to the Mail Recovery Center.