I assume you meant to say that the junk mail was FOR the prior resident and not FROM the prior resident. This little detail makes a big difference in your story.
In any case, when you sign the waivers giving up all your privacy rights to your employer, they are well within their rights to ask the USPS for a list of all the mail you get, which is recorded electronically as mail passes through the sort facilities. The USPS is happy to provide this information for the nominal fee they charge for this service.
Your data is always for sale, and when you give permission for it to be sold, it will be.