In my experience, I have gotten better results by combining the survey with the action of unsubscribing.
If a user goes to the trouble of unsubscribing from something, they really want to, and are having some sort of negative experience that they want to alleviate. To retain as much goodwill as possible with the customer, let them do what they want -- cancel. To gather a bit of data before they leave, such as the answer to "Why?" then present them with a single set of radio buttons with predetermined answers, and one optional textarea to say more. The act of submitting the form both saves the data point and allows them to complete the action they want to perform.
If you really need/want to ask more than one question, then in my experience the most successful response rates are when the questions are presented after the action. Again, this allows the user to complete what it is that they wanted to do; a very clear response on the resulting page that their action is complete, and then a clear (brief) appeal to provide feedback, is more likely to produce results than an up-front action blocker.