The power is out and the lines are being worked on. The line is supposed to be dead. Your solar system is making power and sends it out of the house, back on the grid.
Not that you would want to run appliances with the power dipping out randomly anyway. Maybe to charge a laptop/phone or run basic incandescent bulb/electric space heater/toaster type loads.
Any power either you or your neighbour tired to put into the grid would be immediately consumed by all of your other neighbours (and of course your own appliances) that it would drag your AC waveform completely out of spec (I.e. it should be 230V AC, but your equipment can only supply enough juice to support 0.01V AC). So you’re inverter would shutdown due to lack of recognisable grid compliant waveform. Either that or catch fire from trying to drive thousands of amps (from 100 acre solar farm on your balcony) into your power socket, which would also catch fire, along with all the cable in the wall, well, you get the idea.
In short physics and simple supply and demand ensure that no home scale inverter would ever be able to maintain an even vaguely compliant AC waveform during a blackout.