You would have to check your specific insurance policy to see whether you would get any money back when you cancel.
As a general rule, you only pay for the actual amount of time you're insured. In most cases, that means that if you've prepaid for the full length of the policy and end up cancelling it early, you should receive a refund.
There are a few things to keep in mind, though. If you paid any additional fees to pay in installments or with a credit card, these might not be refundable. If you received a discount for paying early or in full, you might lose your discount and have the full rate applied to the time you were insured when calculating your refund. Finally, you may lose any discounts you received for bundling with other policies such as auto insurance.
Even if you cancel your policy, any incidents that happened before you cancelled should be covered because you paid for insurance during that time.
Some policies may have a provision allowing for a full refund within so many days of starting your policy. If you use this option, you usually won't be covered for anything since you received a refund for the time you would have been insured.