Why does your dodge neon 1996 headlights stay on even if your cars is stop and all the swicth are off and your fuse are ok?

Do the headlights stay on until you disconnect the battery? Or do they shut off after a certain period of time? They may have a timer which keeps them on. Check the owners manual to find out how to change this. If a timer is not the case, your headlight switch is probably bad, or you may have a problem in the wiring harness. I would check the switch first. Unplug it from the back. If your lights go out, you need a new switch.