Unless an insurance company has thrown in a cancellation clause, any unearned premium has to be refunded to you.
In most cases, if you have paid in full for your insurance term you are owed a refund if you cancel your policy at any time before the renewal date. Insurance companies cannot keep the money that you paid to them if they do not provide you with insurance.
For example, if you pay for insurance for January 1st though June 30th and cancel March 31st; you are owed a refund for April 1st through June 30th. The insurance company is not extending you coverage for this time period so you owe them no money for this period.
The only exception to this is if your insurance company has put in a cancellation clause on your policy. Most of these clauses state that if you cancel your policy within the first 60 days you still owe them a minimum of the 60 days of insurance. If your insurance company has something like this they will (or at least should) tell you when you first purchase your policy.
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