A single barrel trap gun is the easy answer, but the back spacer that stops halfway to the breech doesn't seem to make any sense to me. I don't recall ever seeing a shotgun barrel with rib that would need this. Conversely, there doesn't seem to be enough space for a rifle scope, especially a barrel that would be that long on a takedown gun. Leaving half of the spacer off seems illogical as it would only support half the barrel when carrying the case. The only thing that I can see that would work is with a short block where the removed piece was to support the rear of the barrel, but that doesn't seem logical against just having full length support.
Maybe a single barrel rifle with the forearm on the barrel and a set of adjustable sights on the top of the barrel? That's the only thing I an think of that would fit that profile.