k i think i can take a crack at this one. Im currently using a hang on over flow box that runs into a wet/dry filter, then from the wet dry filter the water is pumped from the wet/dry into a refrugium and then at the end of that "refrugium" tank the water is pumped back into the main tank. Ok, what happens here is once you hook the overflow box on the tank, you connect a tube from the back of the overflow box to the wet/dry filter underneath, this is how your water gets into the wet/dry filter.
You will notice when you first put the over flow box onto the tank it is basically 2 boxes. One box goes into the tank and the other hangs on the back. The back box is where you connect your tube to the wet/dry filter. Now to get water from the box in the tank to the box behind the tank, where the water goes into the wet/dry filter, you have a piece of "U" shaped tubing. This tubing is placed so that the water goes up the tube from the box thats in the water to the rear box that connects to the wet dry filter. You will put a piece of airline tubing up into the "U" shaped tubing and create a suction. Now once this suction starts it will not stop untill the "U" shaped tubing is lifted out of the water and the suction stops.
Now to answer your question about how this will start again in a power outage is this. The water flowing out the back box and into the wet dry filter creates a gravitaional pull on the water since its moving down and through the tube into the wet/dry filter. Once your have a power outage all your pumps stop at the same time, so there is no water being pumped back into your tank. So what happens here then is eventually all the water that your overflow box will pick up is now in your wet/dry filter and no water is being pumped back into the tank. You will notice though that there is still water in the overflow box, holding your suction. In other words the over flow box will not drain completely just for this reason, to hold the suction. Now once the power comes back on the the pumps will start pumping water back into the tank and once the over flow box starts to fill up again the suction will take over right where it left off.
This is wet/dry filters and boxes 101.
Any questions please let me know, im at work so i kinda rushed through this.