If you have a GTI and the power cuts, the output will die immeditely. It wont keep running the washing machine.
No GTI will feed power into a dead circuit. That's what inverters do.
GTIs have two error checking systems. One is that to feed power into the grid, it has to lead the voltage and current of the mains. So it "locks" to the grid frequency, and then starts to feed in power slightly ahead of the sine wave. A few degrees ahead in phase, and it puts in a bit more voltage. If the grid is 241.1 it might try 241.3volts. If the grid fails, and its now only the local house that is taking the load, the voltage will immediately rise as the nearly 0 ohm impedance of the grid is no long there to absorb the power. Even if by some miracle the local load is exactly the same as the power the GTI is putting out, the local load still wont have its own frequency reference, and that frequency will fluctuate, which leads to the next error checking system.
The other error checking system is that if the grid is exactly 50hz, it will try to feed in at 50.1 hz. It will try and speed up the grid. Since thats impossible as the grid is a MASSIVE load, the error checking stays low, and the hz figure that its beating the grid at stays at zero.
There is a very specific reason for doing this extra hz feed:
So, lets say the grid drops at a local feeder station, but you have a whole bunch of people on a street all with grid tie inverters. Each one sees the load of the other houses, and the other inverters maintaining the voltage, so as far as the GTI is concerned it still has a grid right?
Except that every single one of them tries to increase the frequency a bit. Since there is no reference anymore, all of them start to speed up. That's then the signal they use to shutdown. Its called "anti-islanding" and absolutely vital to prevent an isolated "island" of houses being kept alive, and stopping power line workers from being electrocuted by what they think is a dead circuit.