My car key is actually stuck in the ignition battery died out after some days after the car wouldn't start. While driving my car told me turn off the engine oil pressure low. but I didn't kept driving until it turned off its self. My car shook itself slow down and came to complete stop then I saw smoke. Is it repairable? It's a 2006 Buick Rainier used I'm the 4th owner. Do I buy a new battery and get oil added? I had it towed home dont know what to do with it.
I'm not too sure if your vehicle does this, but some GM cars kill power to the electric fuel pump when the oil pressure drops below a certain level. Check in a dedicated service manual to see if yours has this correlation. I'm sure you have, but check your oil, also look to see if the pressure sender is plugged in properly. But first check the service manual to see about the fuel pump/oil pressure thing-a-ma-bob. Depending on how far you drove with no oil pressure will depend on how much if any damage occurred. You'll more than likely need to get it running and give a good listen to the engine to find out. Low oil pressure won't necessarily damage the engine. Try giving the battery a good charge first. Just because it went dead doesn't mean it's hopeless.
Generally an oil light is highlighting a lack of oil pressure, often the lack of any oil pressure at all. On many cars it is imperative that you stop immediatly when they come on, and even then it can easily be too late to save the engine.
Most modern cars rely on plain bearings for the crank which rely on a supply of oil under pressure. Without that oil they will be rapidly damaged. Very shortly after that major engine damage will occur (eg, snapped connecting rod)
If you are lucky there is some kind of cut off when pressure gets low as suggested above. However if the vehicle has run low on oil it has probably gone from full oil pressure to zero oil pressure and it still might not have activated quickly enough.
If you are very lucky then new bearings shells will fix the problem.
But given you say the car slowed down while shaking and with smoke I would guess it is highly likely that the engine has serious damage.