However, there are some exceptions to this rule. In some older vehicles, the fuel pump may continue to run for a few seconds after the ignition is turned off. This is done to ensure that there is enough fuel pressure in the system to start the engine. Additionally, some modern vehicles may have a "fuel pump priming" feature that runs the fuel pump for a few seconds when the ignition is first turned on. This is done to ensure that the fuel system is properly pressurized before the engine starts.
If you are concerned that your fuel pump is running when it shouldn't be, you can check the fuel pump fuse to see if it is blown. If the fuse is blown, it means that the fuel pump is receiving power even when the ignition is off. You should then consult with a qualified mechanic to diagnose and repair the problem.