The blower motor resistor is bad and goes to high fan.
It could be the high speed heater motor relay is stuck on or the switch itself is broken.
The reason a heater fan is staying on may be an issue with the switch. It is possible the switch is stuck open. It may be resolved with a good cleaning of the contacts on the switch, or replacing the switch itself.
Switch problem? Cables disconnected?
Yes there is, but it only operates the high speed function.
There are multiple causes as to this condition. There may be a bad switch that is stuck on the high position. The motor itself can have a problem being regulated correctly, for example also.
Odds are you need a fan switch, It is very common for the high on GM fan switches to go out.
It is the resistor, replace it.
The switch had a meltdown or the high speed relay is stuck.
My 1994 did the same thing.....the problem was in the high/low switch....
Run a new ignition switch controlled "hot" wire directly to fan motor
Not knowing what year, make and model you have, I would suspect the heater fan switch and or electrical plug to the switch is at fault.
Replace the blower motor resistor.