The feature is called "Accept/Decline" and it appears regularly in their Premium print editions. Each edition, they focus on a story they liked but had to reject, which then went on to get published elsewhere. They highlight the differences, if any, between the draft they read and the final published piece, feature comments from both the rejecting and accepting editing staffs, and run an essay by the story's author about getting the story published. The essay tells the story of the story.
In my case, the story is 'Doll Love', which ran recently in issue 36.1 (Summer 2015) of Jabberwock Review. 'Doll Love' not online but you can buy it, or read a little about it in an older blog post. And my essay in Carve is also print-only, but their fiction is online and free, and the print edition is measly $12 bucks and comes in the mail and has that glorious fresh-from-the-printer new-magazine smell.
Side note—my essay features a photo of me, which I've always liked and which has gotten a wide variety of reactions, from "great photo!" to "you kind of look like a farmer in this" to "were you constipated when this was taken? You look like you were constipated." If you ever see this photo and wonder who took it, wonder no more: Joe Turic, of Less Gear More Photos. Joe always insists on taking photos of me, whenever we're hanging out. I mean, I can't get him to stop. He's so insistent that I usually pre-empt him and tell him to just take the photos already. "Just take the damn photos already Joe! I know you want to! Go ahead! Do it now. No we can't go eat or hang out with our girlfriends or go do whatever it is we planned on doing. Make sure to get some candids while you're at it!" To the casual observer, it might look like I'm harassing Joe into taking my pictures, but be not fooled, dear readers.