Some months ago I replaced both AC and Fuel Pump relays just as a matter of maintenance. It was also precautionary as I had occasionally had issues with the fuel pump continuing to run for 20-30 seconds after the ignition was turned off. The new relays didn't totally eliminate the problem because the pump would occasionally continue to run, but for a much shorter period of time.
Within the last week, I have had to resort to pulling the fuel pump fuse to stop the pump. With the ignition off, immediately reinstalling it would start the pump again, but if hours lapsed, installing the fuse didn't start the pump while the ignition was off.
Today, I decided to check the relay to see if it was stuck. My test was to swap AC and Fuel Pump relays. After starting the car and letting it run for about a minute, I turned it off and the fuel pump continued to run. I did this test several times with the same result.
I then unplugged the oil pressure sending unit, restarted the car and let it run for about a minute. When I turned off the ignition, the fuel pump stopped running, too. The oil pressure sending unit, as we know, is a backup power supply for the fuel pump in the event the relay fails. Once sufficient oil pressure is built, the sending unit closes the fuel pump circuit to supply power.
So, if you are ever having issues with the fuel pump that just keeps on pumping, try disconnecting your oil pressure sending unit.