I don't think USPS will close completely, but instead of having stand-alone postal offices, they may have to be moved to smaller kiosks inside of larger businesses such as Walmart or your local drug store. However, this isn't the first time the USPS has downsized. A lot of small rural communities had their own small POs but they were shut down and they were merged into the nearest town, which meant, they use the same zip code as the nearest town. IE - Waveland, AR used to have its own post office. Well, it was decided that it was not needed any more. The USPS closed it down and allowed packages to be sent and received from the local gas station until they were able to set up rural delivery routes for that town. When that was finalized, Waveland AR is a different community but it shares the same postal code as nearby Havana, AR.
Now the USPS is looking at closing out lying post offices and setting up rural delivery routes instead. The smaller communities would be using the same postal zip code as the nearest larger community.
So basically your address goes from 12345 No. 1 Lane, No-name, USA 67890 to
12345 No. 1 Lane, Some-name, USA 98765. Your address itself does not change, just your postal zip code.
I wouldn't be surprised if the USPS allows you to send and receive packages from authorized locations that has just the window functions of the PO. Those with PO boxes may still be allowed to use their current PO boxes for a certain amount of time until they are able to find other means of receiving their mail. (most just set up an inexpensive mailbox next to their driveway if they are on a rural mail route.)
Those living in apartment complexes with mailboxes operated by the USPS won't be affected likely.