The usual sequence when firing up a fuel injected engine is that the fuel pump runs for a couple of seconds to "prime" the fuel system when the ignition is turned on, then it switches off until crank rotation is detected. Once running, it will switch off again if the crank stops rotating for any reason.
Once the engine has stopped, it will retain fuel pressure for a long period if not indefinitely, since the only way the fuel pressure can escape is via the now closed injectors or FPR (which closes once flow from the pump stops) and return path back to the tank.
So, bump starting a dead car is possible either because there is likely to be enough energy in even a discharged battery to kick the fuel pump over for a couple of seconds or, failing that, because the fuel rail remains pressurised anyway.
Some Omegas (non-dbw V6s and some of the 4 pots, IIRC) don't use a priming procedure, so the fuel pump doesn't run until cranking is detected. I know for a fact that a 3.2 runs the fuel pump for a few seconds when the ignition is switched on.