HVAC blower often (but not always) gets stuck ON.
If there is a circuit board with relays, then it sounds like a faulty (broken return spring) fan relay. Other furnaces use a bimetal switch that extends into the heat exchanger. When the furnace warms up, the bimetal arm would bend and make contact for the blower motor. As the furnace cools, the bimetal arm would straighten out and turn off the blower. A replacement would be needed. It is usually located all by itself with 2 or several wires, and removes easily with 1 or 2 screws.