[D13]

The ECM fires the fuel pump relay to build pressure fuel for start up. Once running, the ECM drops the circuit and the relay is fed by the oil pressure switch being closed. If the switch is bad, unplugged, cut wire, or no oil pressure, no signal to the relay and no fuel is pumped. Once the start up pressure is gone the engine stalls.
My bet is if you measure voltage to the pump it goes ot zero once running, indicating the oil pressure switch is bad or disconnected.
If the pump is getting power, then the in-tank sock or filter, or a tired pump, are most likely.