By not having a physical mailbox. Nothing says that you have to have a mailbox, and without one the USPS won't deliver mail to your house. Also, I believe that they have some sort of permanent forward that the local postmaster can put in so that if you don't have a mailbox at home they'll send it to a PO box.
I often wonder if those outages aren't sometimes caused by hackers to begin with. Publicizing them as hacks would only serve to cause panic, and let other hackers know how vulnerable their systems are.