TSTAT wire through vent?

So this damper zone wire was run through the vent pipe installed since the furnace was in the hall closet. Is this ok? I am guessing not since the vent is charged with removing combustion gases. Just need to get some other opinions. Thanks & God Bless.

How could that vent be discharging flue gases when it is not connected to the exterior

It is charged with removing gases at the bottom of the closet. Otherwise, what is it’s purpose then?

Combustion air?

There should be no gases in the bottom of the interior closet, there should be two vents one a foot below the ceiling and one a foot below the floor area they are for providing combustion air to the furnace burners, I assume a 80% furnace with open burners. Thermostat wires are not plenum rated but for the combustion vents it would be alright for them to be inside the vent

Yes this was the vent that was a foot from the floor.

It did seem like it would be ok. Just needed to get a second opinion. Thanks.