When a preapproval is cancelled by a customer through their PayPal account you will receive a notification from PayPal. You will want to handle it the same way that you would a refund.
Go to the Preapproval screen in JVZoo (Seller->Reports->Preapprovals) and look up their order. Then cancel the Preapproval through JVZoo.
This will sync up the JVZoo system and any external programs that need to be notified, cancelling their access or you can manually remove access if that is how you have your product set up.