Do the same thing they do in commercial buildings frame all the way to the floor above and finish it with drywall or wood
http://www.firehouse.com/article/10471100/basement-fires-difficult-challenging-and-dangerousAnother hazard is rapid fire development and spread. Many basements have no walls and doors. Many basements in private dwellings and commercial buildings alike are wide-open areas with large amounts of flammable stock, furniture and other debris. Once a fire takes hold, it can rapidly spread across the ceiling in seconds and trap or threaten firefighters operating down there.