Some fireplaces and some high efficiency gas appliances suck in raw outside air and exhaust dirty air. If you really wanted a basement coop, and you're handy, you could build one that is "weather tight" against indoor home air and uses abundant ventilation from outdoors. Insulate the coop to keep your heat in the house, and just think of the coop as "unheated outdoor coop", even though technically its inside your foundation's walls. Probably needs an attached maintenence room in the air flow too (a place for you to approach the coop and open an access door) so whatever you stir up taking care of things is vented to the outdoors. That leaves their run. Do you have enough basement room for all that?