The process involves:
* Ignition System: The ignition switch itself is the primary control. Turning the key to the "off" position breaks the circuit powering the ignition coil, stopping spark to the cylinders.
* Fuel System: The fuel pump is controlled by a relay and the computer (Powertrain Control Module or PCM). When the ignition is off, the PCM signals the relay to turn the fuel pump off.
* Powertrain Control Module (PCM): The PCM is the "brain" of the engine. It monitors numerous sensors and controls various systems, including fuel delivery and ignition timing. A malfunctioning PCM could theoretically prevent proper engine shutdown.
* Various Sensors: Many sensors (crankshaft position, camshaft position, etc.) provide data to the PCM. Problems with these sensors could affect the engine's ability to shut off cleanly.
To diagnose a problem where the engine doesn't shut off when the key is turned off, you'd need to investigate these systems, checking for issues with the ignition switch, fuel pump relay, PCM, and related wiring. A mechanic with diagnostic tools would be necessary for a proper diagnosis. You cannot simply locate and replace a single "auto shutdown relay."
