It would be interesting to find out what exactly the USO (universal service obligation) of the USPS says about this. I found this:
The Postal Service’s USO includes a requirement to provide mail services to everyone, regardless of where they live, and for at least one mail product, at a uniform price.
If this is also valid for Puerto Rico (and why not) it would mean that everybody should be able to get mail delivered.
In the rural areas there are the mailboxes where contractors (Highway Contract) deliver mail. We have one of those boxes, it's about a mile from our house. The contractor, a very friendly lady also delivers packages at the houses in her area. She needs, of course to know who lives where and after that she delivers. Always!
I think, Richvide, that in your case you should check at the post office that is responsible for your area how the mail delivery is organized and how you can get your mail delivered. The Postmaster should be able to inform you.