From what I understand, most homes that are connected to both solar and the grid require the grid to be active to produce solar. This is for two reasons. One, not to endanger lineman working on the grid. And two, the solar AC cycle must be synchronized with the grid AC cycle. Are these homes not also connected to the grid? Or is there some technology that addresses these two issues that are in use in Puerto Rico?
It's becoming more and more common for PV systems with a battery system to be able to work in an islanded mode, and more importantly - they're legal and code compliant to do so.
When the grid goes down/out of spec, they disconnect the home from the grid and continue to power locally.
Examples of this include Tesla and Sigenergy.
Some are able to do this in very short periods and able to operate effectively as a whole-house UPS. Some will have a flickr of the lights and maybe some sensitive devices will restart. Others will take some period of time to disconnect from the grid and run in islanded mode.