In a situation such as this, when asbestos material is not properly removed, asbestos fibers could have been released and become airborne. The fibers can also mix with the dust and remain in the basement area for an indefinite period of time. If asbestos fibers are inhaled or swallowed, they can have serious effects on your health, which may not appear until 15 or more years later. Asbestos can cause asbestosis, a scarring of the lungs that leads to breathing problems and heart failure. It can also cause cancer of the lungs and mesothelioma, a rare cancer of the chest or abdomen lining.
Special regulations exist for the removal and disposal of asbestos.
More information on asbestos can be found at the U.S. Consumer Products Safety Commission web site.