Once a policy is issued, the insurance company except for reasons specifically stated in the policy can not cancel it, and state laws usually limit what a company can include in the "cancellation" provisions of its policies. Typically, policies will be subject to cancellation only for failure to make required premium payments or for some type of serious misrepresentation or fraud by the policyholder.
Most property and liability policies are issued for a stated policy "term", such as six months or one year. The limitation on cancellation mentioned above applies only during the policy term. Insurance companies usually can decide to discontinue or "non-renew" these policies at the end of the term for any reason except a reason that would be prohibited by law (also, in a few states an insurance company may not refuse to renew certain types of personal insurance). In most states, an insurance company must give the policyholder a written notice at least 30 days prior to the end of the policy term if it intends to non-renew a personal auto or homeowner's policy.