By default, when you hit Publish on a Storify story, it becomes publicly available to anyone visiting its URL or clicking on it from your Storify profile.
If you're logged in on Storify, look at the top of any published story you own. You'll see a number of buttons. Click the "..." button to reveal additional options for the story, including "Revert to Draft."
Note: "Draft" stories are only visible to the logged-in story's owner. If you revert a published story to "Draft" mode, its URL will not be accessible to others. Additionally, if the published story has been embedded on other websites besides Storify, reverting it to Draft status will break the embed until the story is published again.
For more information on Storify and Storify Enterprise features, visit Livefyre's Answers area. For questions or issues related to a specific story or account, contact firstname.lastname@example.org