It's not so much being unplugged as it is sensing whether the mains power is down. If it is, they stop backfeeding immediately, just like hardwired solar inverters do.
If this weren't done, there would be risk of electricution to anyone working on wiring in the house or on the utility distribution network.
It's also important for the male plug prongs to not be live when unplugged.
They have to sync up and feed power in phase with the grid when its up as well, in the case of net metering setups.
Even without net metering.
Yes, the "balcony" style setups, sync to the power outlet of the house, which could be the grid, or it could augment a generator when the grid is down.
I commented a little too quickly and left the nuance out. Your answer is much better!