What can/should be done to mitigate asbestos danger after a disturbance?
Professional air monitoring is the first step: expect a bill in the range of $500 (a technician stays on site for the entire hour or so test).  A little compressor draws air into a sampling can, which is analyzed in a lab.  They physically look for captured fibers and can find a single fiber in a sample. 

Asbestos removal is surprisingly expensive, and must be done by a licensed firm (at least in the USA).  In California USA I was quoted $750 in tipping fee alone for one square foot of asbestos paper, though a bigger firm can combine with other jobs.  Everything is registered and tracked.  As usual get multiple bids: you may have trouble finding a firm willing to clean up after someone else's mess.  The full procedure involves huge quantities of plastic, creating a negative air pressure zone where the worek is done.