Cancelling a subscription only prevents it from being renewed and you continue to have the service until the expiration of the term you have already paid for. You are never automatically refunded money for any remaining term of a subscription no matter if it is from Apple or any other subscription you subscribe to.
You can certainly try requesting a refund. In most cases all transactions are final, but in some cases Apple may provide a compassionate refund. It should never be expected though.
Request a refund for apps or content that you bought from Apple - Apple Support