What happens to mail sent via USPS that does not have a stamp or a sender return address (only a destination address)?

If a letter has a return address, it is returned to the sender for postage. However, if there is no postage at all, and there is no return address, the postage due is attempted to be collected from the addressee. If the addressee refuses to pay it, then the undelivable mail ("dead mail") will go to a Mail Recovery Center (Formerly known as "Dead Letter Office") in Altanta, GA or Saint Paul, MN.

Mail Recovery Centers are the only place where US Postal Service employees have the right to legally open someone else's mail, otherwise it would be a federal offense. The Mail Recovery Center clerks will typically only open letters that are determined to be "valuable" by an automated scanning machine that scans for currency, checks or other items of value. All parcel packages are opened and inspected by hand to try and find some clue as to who sent the item. They will try to identify who the sender was through a name, a phone number, a check or any document within the letter or parcel. If they do find the rightful owner, they will forward the item to the sender, which happens about about a quarter of the time. If there is no identifying information, then the mail is stored for at least 90 days, then valuable mail is either given away to charities, or sold at auction. All else would most likely be destroyed. In the past the US Postal Service has used eBay.com to auction off items considered valuable.