The device looks for an existing signal from the grid, and if it doesn't find it, it stops feeding power. It even waits for 3-5 minutes before trying again plus some random jitter to avoid thundering herd. It's been a standard in Europe for a while and now finally in the US. This of course depends on the utility and state as not all of them have adopted it but it's quickly becoming the standard everywhere.

IEEE 1547 (interconnection behavior), UL 1741 (inverter product safety), UL 3700 (plug-in solar). (also there are newer revisions you need of some standards like UL 1741)

I imagine the solar panel will detect when the circuit it is plugged in to is de-energised and stop supplying supplemental power to it.

In Germany, where this kind of plug-in solar panels is very common (1.5 GW installed power) it is mandatory that the inverter powers itself down as soon as the grid is offline/disconnected. It has to be so fast that you can savely touch the plug after unplugging it. I guess it's standard everywhere.