What happens when a car is running just shut off?

most likely your ignition switch is bad. is not breaking the circuit.

Or your vehicale is running so rich (air to fuel ratio) that the catalitic converter is glowing red hot from working so hard to burn up the unburned fuel. So in theory even though you turn off the ignition which usually kills power to the coils ( the source of ignition) your car will continue to run because now the source of ignition is taking over by the red hot cats. This is most common on carbed vehicales, because fuel injected vehicales supply of gas along with ignition is killed when the ignition is switched off.