There is a fuel pump relay that supplies the power. I can check my manual later to see where it is and what feeds it power. When you first start the motor it closes that relay for long enought to start and then if the computer doesn't tell it it is getting air, etc, it will shut it down. The idea being if you get into a wreck or something it won't keep pumping out fuel.

1997 T-100 4X4 Xcab,Warn Hubs
02 Camry LE
2008 Yaris