that is an outlet from the heatpump putting hot/cold air into the space between the downstairs ceiling and the upstairs floor. They cut a hole in the downstairs ceiling by the woodstove I'm assuming to let some of that hot/cold air out...
It attaches to the main hot duct about 3' from the furnace then runs maybe 2' to the end you see in the picture. The end is roughly 3' from that hole in the roof.
I spent a lot of time in the attic looking for air leaks and strange ducting before I put R40 on top of everything so I don't think there is any ducting from basement to attic going on but who knows. I did find that they had done a drop down ceiling over the bath tub that dropped roughly 12". They then put 6" of insulation in it so the top 6" of the walls beside the drop down had 1/2" of drywall between inside and attic air. whoops... No wonder the bedroom right there was so cold in winter. a 6'x6" strip of wall right near the ceiling with zero insulation to outside... That was at least an easy fix. I filled it with fiberglass batts and then went over the entire area with the R40. I also put up a little flag to remind me when crawling up there that there is 3' of insulation so don't just fall in
