I tend to think exactly the opposite. When I try to cancel I want to see a page that lets me cancel, not a survey to ask why I'm cancelling. It feels like a last ditch effort from a clingy, depressive/low-self-esteem lover.
That way your cancel's done and dusted but with the option to feedback if you fancy it
I've seen a few sites that don't make it clear that you have successfully cancelled and act as though the survey is still required, so don't do that. Make it clear the user has finished cancelling and this is an extra step they can take if they'd like.
Caring is important, even if you're caring about your business in the grand scheme of things