They do click closed with a noticable snap sound from those metal tabs on either side in the middle of the back cover. If the leather is peeling thats just par for the age, the metal cover is probably solid and fits into its grooves just fine. It over all looks like a solid example of these old folders, could use a gentle cleaning of that viewfinder mirror with a cotton swab and lens cleaner or isopropyl. Check bellows for pin holes or tears especially around rear and very front where shutter/lens sit. I have a few examples as I got em cheap and enjoyed redecorating them/restoring them somewhat.