Feng Qian , a few things that can cause car headlights not to turn off include faulty headlight switch, multi function switch, daytime running light module, light sensor, relay.
Tracking down the fault can be complicated, there are so many different types of headlight systems out there. Some cars are designed so that if the engine is shut off while the headlights are on, they will remain on for a specific amount of time. If your car has this system, it may have failed, and you might want to try shutting the headlights off before turning the engine off and removing the keys to see if that helps. You may want to take vehicle into a good shop, have them diagnose and estimate repair. Good luck.
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