Normally if you blower will not shut off, you have a bad resistor or relay...most likely the relay...
BAD FUSE SOUNDS NUTS BUT IT IS?
Climate control blower motor was the fix. The part cost 441 dollars.
The most common problem when a car's heater fan doesn't shut off when the car is shut off is that the resistor on the blower motor has gone bad. The fuse that powers the resistor should also be checked.
If the fan runs with the HVAC panel shut off, the blower resistor power module has failed.
The blower in a 2007 Nissan Quest may not shut off due to a faulty blower motor resistor, a malfunctioning climate control module, or a stuck relay. If the resistor is damaged, it can cause the blower to receive continuous power. Additionally, issues with the vehicle's wiring or a short circuit can also lead to this problem. It's advisable to have a professional diagnose and repair the issue to prevent potential electrical damage.
Have your blower motor resistor or blower motor checked out
Generally automotive blower motors are designed to run on the lowest speed even though the heater is turned off. The purpose is to circulate fresh air into the cab.
when my car did this it was a blown fuse
The blower control module is defective.
faulty blower module. Under hood not far from blower motor
Probably the control unit mounted underneath the relays by the firewall. Get a used one somewhere, but get a new blower (parts store item) to go with it. That might save you from having to buy an other controller.
Ifit has the c68 option (auto air) check the blower control module under the hood