Your right in thinking its connected to the mid pipe and runs all the way to the cat. The backbox can be seperated from the centre section by a join just above the rear trailing arm. Theres a sleeve that can be opened so they can be pulled apart.
Its a very common problem, its probably happened to all 172s. Near to the joint at the back of the backbox is weak. The joint itself onto the centre section is normally ok, its the bit of pipe thats poorly welded on the back of the backbox that breaks. The bracket on the backbox can also break as its very heavy. The centre section also comes apart from corrosion.