Asbestos abatement: should I decide to re-clean?
Your decision to re-clean your building or home should be based on the results of any testing that is conducted and the opportunity for exposure from any remaining asbestos fibers. Clean up entails vacuuming the area with a vacuum equipped with special filters (HEPA filters) and wet wiping affected surfaces. A New York State Department of Labor licensed asbestos abatement contractor should be employed to conduct re-cleaning.
Courtesy of the New York State Health Department

Lawyers: Asbestos Health Problems include Lung Cancer and Mesothelioma