Even if the company agrees to keep the home insured at a more reasonable cost, make sure you get a completely new policy document that proves you have coverage on the empty or unoccupied home. We advise you strongly, do not simply take the agents word for it. Normal homeowners insurance policies are not set up to provide vacant home insurance and many exclude even short term vacancy.
The cost of vacant home insurance is high to begin with because of increased risk and fewer market choices, but the cost some companies are "offering" to clients to keep the home insured after it becomes empty or vacant is astronomical. What's more, we have seen the level of coverage drop from an all risk policy to what is called a dwelling policy for vacant homes, a limited policy form.
In almost all cases where the home goes empty, seek out an insurance policy that is designed to meet your exact needs not a square policy someone is trying to use for a round hole to make a little more quarterly profit.