3. Publish the category by checking off the "Published" checkbox and save your changes by clicking on "Save & Continue Edit". You can keep this tab open since after moving all the items to the category, you will need to unpublish the category itself.
4. Find the item that you would like to permanently unpublish from the website and move it to the DO NOT PUBLISH category.
5. Unpublish that item.
6. Go back to the DO NOT PUBLISH category tab you kept open on step 3, uncheck the "Published" checkbox, and save your changes.
By doing the steps above you first publish the category in order to be able to add items to it, then work on the items, and then unpublish the category itself back so it remains inaccessible to customers.
Unless you are working on moving the items to that category, both the category itself and all the items in it must always be unpublished - that is the only way for the customers to never discover those items.