Whenever the buyer moves into their new home before escrow closes or a seller stays in their old home after they’ve sold it, everyone needs to make sure that the home’s current home owner’s insurance covers the situation. Usually, someone needs to call the company up and change the policy. (Make sure the company gives you a document noting this change.)
If a buyer moves in/rents the home before close of escrow: seller, make sure you call your insurance company up and change the policy so that it covers the buyer renting your home. Your insurance may change from regular home owner’s insurance to insurance for a rental.
If a seller stays in the home/rents the home back after close of escrow: buyer, make sure you call your insurance company up before escrow closes and make sure the policy will cover the seller renting your new home. Again, the insurance company may charge this time as rental insurance coverage. Make sure to call your insurance company up again before you move in, and change it so that you are covered when you move in as an owner occupier.