Have a plan to ensure that asbestos will not be disturbed during the renovation. If you believe it is unavoidable, you should contact a licenced asbestos removalist company to get rid of asbestos before you do your home improvement project.
If you accidentally break asbestos while in the process of renovating, the safest thing to do is remove dust using a damp cloth. Wipe the dust and put the fabric in two plastic bags. Secure them together to make sure that the fibres cannot escape. Put them immediately in the skip bin.