I am one of those 3rd party contractors that delivers packages for UPS and FedEx while fulfilling my USPS contract. UPS and FedEx drop off packages at my home and scan them as delivered, I sign for them and hand them one part of a triplicate receipt. When I deliver the packages for UPS and FedEx I have the customer sign the remaining 2 copies which they get one of. I'm not sure if that is a normal procedure for other contractors or not but it seems UPS and FedEx alike would have some form of assurance method to insure delivery.
My best suggestion to you and anyone else that receives their UPS and FedEx packages via 3rd party carrier, would be to contact your closest UPS or FedEx delivery hub or their distribution hub and and follow the trail to the last of their carriers that scanned the package. They should know how to contact the 3rd party carrier, if you don't already know who that is personally.
This explains why often times a package will show as delivered but I won’t get it until the following day, from a third party carrier.