There are 3 considerations when moving out of your home and deciding if you should keep insurance.
First off, if you have a mortgage on the property, then it is likely that in your note and loan paperwork it will state that you will keep fire and liability insurance in place with the lender as loss payee.
But if you don’t have a loan, then there are a few considerations. First off, you are always best off with insurance. Even if you have a renter in the house, they normally only have insurance that covers their personal belongings, also known as renters insurance. If you move out of your home and it is vacant, then you may want to discuss with your insurance broker if you should change your coverage.
Most of the time a homeowners policy is only valid if the homeowner is living in the home. Insurance companies don’t like to insure vacant homes for the obvious reasons that they tend to get broken into, and because if something goes wrong (i.e. a leak or a fire), a homeowner who is actually home will likely be able to limit the damage. Many insurers will limit the amount of time your home can have coverage as vacant, after which they will either cancel coverage, require an amendment to the policy, or issue a completely new policy.