We're getting several things mixed up here.
First, the tailcone. It is an aerodynamic faring at the rear of the airplane. On all DC-9's and early MD
-80's, the tailcone is conical in shape. On most MD
-80's and later airplanes in the DC-9 family the tailcone tapers to a vertical fin also called a boat tail fairing. The boat tail fairing results in lower airframe drag.
There have been several cases of airplanes losing the tailcone in flight or on landing due to improper installation of the tailcone. Occasionally, someone on the ground attempting to lower the ventral airstairs (on airplanes with them) will pull the wrong handle and jettison the tailcone instead.
Second, fuselage failures. All of the DC-9 family airplanes are susceptible to failure of the fuselage aft of the wing if an exceptionally hard landing is made. If you do it really really hard, the fuselage forward of the wing may also fail.
Often, if the airframe is relatively young, the airplane will be repaired and placed back into service. I've been involved in the repair of a DC-9-30 that got bent, but not quite broken. I don't not know of any serious injuries or fatalities occurring due to a fuselage failure on landing.
Third, rear pressure bulkhead failures. At the rear of the cabin is the rear pressure bulkhead. It is susceptible to cracking in the curve Tee shaped member that attaches the bulkhead to the skin around the periphery of the bulkhead. The Air Canada DC-9-30 airplane incident flying from Boston to Halifax is an example of this kind of failure. This is one of the structural areas on the DC-9 that has been subject to Airworthiness Directives. The failure may be due to fatigue, corrosion, or a combination of the two.
Fourth, engine pylon failures. The engine and its pylon are supported by two bulkheads in the fuselage. The forward bulkhead is in the pressure vessel and is also used to support the forward wall of the aft lavatories. The aft bulkhead is aft of the rear pressure bulkhead and you could see this bulkhead if you ever get back in that area. There have been failures (or partial failures) of the attachments between the pylon and bulkhead with result in the engine sagging usually at the forward bulkhead. I don't think an airplane has ever lost the engine in flight, but there have been several close calls. People who have detected the engine sag, say that they sense that something is wrong before they realize that the engine is sagging. The engine normally is canted forward end up and sometimes a person has to look at both engines and compare them to be sure if one is sagging or not.