If it comes to insurance, do what I do. Call your insurance and get a rider for the time that the work is on going. Also, get a release after the work is done from the contractor PRIOR to paying him in full. If he rented equipment he needs to tell you that and if he had to get any supplies he needs to tell you that. He needs to give you the release to start the clock on any claims. Now some are going to say this is too much trouble, but if you don't get the release you are not going to be able to start the clock on the deadline for filing Mechanics Liens. Once that period is over you are safer.

But get the insurance rider, they are very inexpensive.

Yep ;)
I worked with some mortar one time that had a little bit of cement in it too ;)