Usually a bad fan motor relay not telling it to shut off
If it is running after the engine is shut off, the relay has failed. It is bolted to the frame under the air cleaner.
Engine overheating or cooling fan running all the time.
The radiator fan should not run after the key is shut off. The normal cause is a failed radiator fan relay.
Radiator fan inoperative, thermostat stuck closed, coolant low, radiator restriction, etc.
check the cooling fan sensor somewhere attached of the fan housing.
cooling fan relay is bad?
to dissipate the residual heat in the radiator it will shut off automatically
The radiator cooling fan will run to cool the radiator to below the fan turn on temperature. You may want to have your cooling system checked if it happens regularly as your Buick may be running hotter than normal when driving.
Either your engine is running hot or the fan switch in the radiator has failed or the relay is stuck.
The two relays are located on the right (passenger) side of the fan shroud. 99% of the time the reason the low speed fan is not running is due to the fan motor itself and not the relay(s).
Do NOT srive it unless you have to! Call your local Chrysler company and ask them if it's ok to drive it to them. Get it fixed and you're good to go!
Low coolant, failed water pump, thermostat, plugged radiator, inoperative radiator fan, head/head gasket.