Dad's house is the same way, over 100 years old, and the old 3rd addition is just as you mentioned, but it has vents to the outside(thru concrete wall, which isn't in very good shape).

I'm too fat, to get underneath(into crawl space), thru the old broken foundation wall(limestone) of the original basement(looks to be broken out, for some old HVAC ducts) They must have had a skinny guy install those pieces of sheet metal ductwork.