After installing thousands of doors we have pretty much seen every situation. Attached are some pictures to show how to do a barn door on a protruded wall. True there are some that it is not possible but others just need some creativity. See some images below where a door was installed on a brick wall but the brick wall protruded a good 6″ out from the drywall part of the wall. This required furring out the wall to bring it flush with the brick. From the front view it looks just fine, included is a close-up of the furring so you can see how we achieved this. If you have other questions reach out to us we are happy to help. And don’t worry usually you CAN do a barn door on a protruded wall.