With all the big news about Netflix, Hulu and other video apps not requiring Xbox Live Gold anymore. Many gamers were wondering if they could cancel their Xbox Live Gold membership and get a refund for the unused portion. The answer is yes, but there is a catch: Of course no more free games with the Games with Gold, but any existing games you downloaded will still work for the Xbox 360. Xbox One games will not function after you cancel Xbox Live Gold.
Will I be able to cancel my Gold membership?
Yes. Once the Xbox One and Xbox 360 system updates become available in June, Xbox Live Gold members who purchased a paid membership before that day can cancel and receive a pro-rata refund of any unused remaining days between the date of cancellation and the date their paid Gold membership ends. Cancellation and pro-rata refund requests must be made by August 31, 2014 and require six to eight weeks for processing. Free or trial Gold memberships are not eligible for a refund. To request your pro-rata refund, please click http://support.xbox.com/contact-us after the system updates become available in June.
From the Microsoft Xbox Live Changes FAQ.