I purchased a 2005 Mitsubishi endeavor limited, when I turn my headlights off and turn my vehicle off the headlights stay on. I went out this morning to check the car out and found my battery dead.

I agree with earlier post. I have found that in Mitsubishi relays do have problems. But considering the age of vechile an depending on where you live you may use lights more than other place an it is normal wear. Sometimes you can tape on that relay an feel it humming or vibrating. Mostly they just hang up an wont go out.

Your best bet is to get a hold of the wiring schematic and see what items control the on/off cycle of your lights. If there is a relay involved and it goes bad, it might just stay in the closed position and leave lights on to drain battery while car is not in operation. Will be somewhere in the ignition circuit and it should get turned off when you remove the key.