The heater blower motor coniues to run even after I turned it off and stays running when the key is turned off. What is causing this to happen?

Question edited for clarity.
Question moved to model category.

Seems to be a known issue.

Blower Wont Shut Off - 1999-2013 Silverado & Sierra 1500

GM-Trucks.com https://www.gm-trucks.com > forums > topic > 11348...
May 9, 2010 - If the blower resistor is shorting prematurely then you most likely need a blower motor due to excess current draw.

Chevrolet Silverado 2007-2013: Why Won't My Blower Work?

ChevroletForum https://www.chevroletforum.com > how-tos > chevrole...
Another common problem will be the blower motor will stick in the ON position and never shut off.

Blower Motor Won't shut off ' GMC Truck Forum

gmfullsize.com https://www.gmfullsize.com > ... > Maintenance
Jan 17, 2011 - While driving today blower motor Kicked out, I turned up the fan speed and it kicked back in. Got to my destination, turned off the key and the ...

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Heater/blower Won't Shut Off - Ask the GM Technician

GM-Trucks.com https://www.gm-trucks.com > forums > topic > 72853-...
Jan 11, 2008 - Cause is a mis-positioned harness from the blower motor assembly to the right I/P fuse block C4 causing harness rub through at right I/P metal ...

Most would say it is the Blower Motor Resistor or a relay..And possibly the dash heater control knob..However it is running all the time even with key off..This means it is getting power all the time from somewhere..It sounds as if wiring is crossed..Did you have to change wiring plug in connectors..?..

posible blower resystor and relay is all une piece mounted nes blower motor

replaced ac and heater blower motor relay, because it will not switch off power to blower motor causing blower motor keep running and pull down the battery.

They don't use anything in common except the controls and the engine coolant in the heater cores. The car is old enough that the blower fan motor is just worn out and needs a new one. I'd try turning it on and wrapping on the motor even a warn out one if vebrated might come on. The blower control module is a failing peice and is quite expensive. If it did fail tough is because the blower motor as it wears out draws more power and the fan blade itself accumulates dirt and makes the motor draw more to turn the heavier fan. I'd test for power and ground right at the motor. I'd also just run a wire to it and see if it'll run. With the key on thiers power to the motor though the blower relay and the controller turns on the ground. You might find that the powers their but the ground is'nt. Put a ground jumper to it and see it run and if and amp meter says it's drawing less that 10 Amps let it run for awhile and see if the Amo draw rises as the motor as it warms up may get tight and draw more power after it's had time to warm up. GM heater motors have been doing this for a long time and it's nothing new. The wire connectors are suspect everwhere theirs a connection as the connectors heat up over time and fail. Once the problem is corrected and you paid the big money( maybe) change the blower motor so it doesn't happen again soon.

Do you mean heater fan or cooling fan?

You MAY have an "Ignition Switch " thats bad.

the blower motor speed control module is defective, replace it.

all electrical(radio wpiers and blower motor) will stay on until drivers door is opened.

Your blower controller has failed, It is located in the heater duct, above and to the passanger side away from the blower motor. There are two connectors that plug into it and two screws hold it in place. Other GM cars of the same vintage will use the same controller IF they have automatic air system.