Unlike radiation, there's no safe asbestos exposure, if you're really unlucky a single strand can screw you up. On the other hand, of all people having worked at asbestos facilities with early 20th century approach to PPE only 20% developed mesothelioma and 10% died from it.
Thinking before swinging your drill will get most people safe enough not to worry about it.
Thinking before swinging your drill will get most people safe enough not to worry about it.