1993 buick roadmaster; blower fan motor stays "on", after ignition is off

blower fan motor continues to operate, after ignition turned off

Normal, as long as it turns off after the engine cools off a little.

I think the poster is referring to HVAC blower motor.

The problem might be from a defective high speed blower motor relay. This relay has constant power supplied to it thru a fusible link. So if the relay sticks the blower will continue to operate even if the ignition switch is turned off.