Fuse on a/c blower always hot when the blower is high stage or Full

non in USA< so no books to read to you from here.
fuses are first we check them all.
and in USA we can scan the car OBD2 AND it MAY SHOW WHY.>?
blower dead , as in silent even on high.?????
try high speed mode blower first, if that works and lower speeds not the resistor block is bad. if all speeds dead , see below.
is this car manual controls or climate controls
the later uses no resistor block it uses powerful controller..
bad blower, or bad controls.
the resistor block if present at all, is on the output casing the blower
as the resistor gets super hot so is cooled by the blower air flow.

the blower can be hot wire tested in place.
it has only 2pins, one is ground other is 12vdc.
so we hot wire it using 15amp fuse jumper and yell, see it is good easy.
now know input to blower is dead.
we discover if manual or climate controls are here and I can not do this in USA<

I looked at 05 avalanche 1500--automatic hvac. The blower fuse is hot all the time. The fuse has an input leg and output leg, even if the fuse is blown, the input leg would still have voltage. If no voltage, you could use jumper wire connected to voltage on the output side of fuse cavity to see if blower would work. If you use jumper, use an inline fuse.
Yes, it could be something wrong with fuse box or wiring circuit?

check fuse first
then scan PCM , oops you didnt and the BCM does run this stuff.
so not scanning it , you miss all those FACTS.

the blower is dead. (aka , not spinning , or silent)
on all cars made the answer is the same.
blown fuse, fuse marked BLower, is blown. LOL.
controls not turning it on, controls failure.
blower bad. (motor) hot wire it in place to test)
wires to any of the above.
or the resistor block bad, (if it works on high but not low)
i have the schmematic in hand.

the HVAC relay pulls in by command of the BCM
the relay then sends 12vdc power to the blower via fuse 41
the blower is now hot full time.
the blower then needs a ground to spin (run)
on high, the ground G601 via the speed knob,switch makes that ground connection, so if the fan dont spin and say the fan is ok
then the relay is not closing or the fuse 41 is blown. (why not look at the fuse first for all electric fails)
the BCM sees you, turn fan on, (heat or cold)
and closes this relay, on the left.
if the relay does not close, (and coil is ok inside)
the the BCM didnt see those HVAC requests.
use a scan tool and look for BCM errors..>??????

IF the heater fan is not working it is most likely the heater fan motor that has failed.

look in the fuse panel there is a fuse for blower high and blower low check the one for blower low the location is on the inside of the fuse box lid

I would check the fuse to the blower motor, if thats good then check power at your blower connector. In some cases the final stage may have gone out. Generally that would cause the blower to move on its own from low to high and back to low, in worse cases its either on full blast or off in your case. Good luck and let us know what you found!

Fan Motor drawing to many amps. .

could be blower motor resistor or blower motor control switch is bad.

Most common cause of this problem is a bad climate control power stage. The power stage control the speed of the blower fan on different settings, if it goes bad it defaults to full blast. There is a small chance the climate contro lunit itself is bad but more than 90% of the time, it is the power stage. It is located near the blower fan under the dash in the passenger footwell area. It makes it much easier to remove the glove box and knee bolster as well as the cover panel. It is rectangular in shape about 1.5" x 3" and black.

Run's continuously ? High speed , low , med 1,2, 3 . ????
Probably the high speed relay contact's stuck closed . The fuse for the high blower is hot at all times , low blower fuse is hot only with key on. It sparks becaused the motor turns on . If it had a short the fuse would blow . The blower motor relay is part of the resistor pack near the blower motor .