Most cars do not leave their headlights on when the ignition is off. Instead, they turn the lights off automatically after a few minutes, when the doors of the car are opened, or the car is put into park (for an automatic transmission).
Some higher end cars do have a feature to leave the lights on for a predetermined amount of time after the engine is turned off. This is useful if you want to walk up a pathway towards a house without having to walk in darkness.
