it happens to every shooter at some point. A cartridge case splits (due to age, exposure to chemicals or being re-sized too many times). This is not a problem when it happens on your reloading bench, but when it happens in the chamber of your gun, it can be a BIG problem.
This is a re-enactment of a broken shell incident that happened to me several years ago. I did not think to document it at the time.
While shooting my Winchester Model 94 Saddle Ring Carbine, I had a jam, I could not get a cartridge to load, so I tried another one, same thing. I looked in the chamber and found that part of the case was stuck in the chamber. This is what the half that ejected looked like, it was cut almost exactly in half.
So I took the rifle back home and began searching the internet for a broken shell extractor for a 44 Magnum. A broken shell extractor is designed to fit in the chamber just as a cartridge would, the base is held against the bolt by the extractor and the body is smaller that the cartridge, so it may fit inside and grip the mouth of the stuck case. The one below is from Brownells, unfortunately they no longer have them in 44 Magnum, no one does (or at least didn't a few years ago when I was looking)
The problem was made that much more difficult by the fact that the chamber in a model 94 Winchester is shrouded by the receiver and there is limited access.
I tried using a brass cleaning brush. I inserted the brush from the muzzle end, no luck it wouldn't budge. I tried the chamber end, pushing the brush just past the broken case. I pulled pretty hard before the brush "bent-over" against itself, still, the broken case remained in place.
I came up with the idea of using a tap. I went through my selection of taps and found one that would thread its way into the cartridge case without cutting all the way through the brass (which would ruin my chamber). A 7/16" x 20 NF tap was a perfect fit.
I dis-assembled my gun, removing the bolt and cartridge elevator.
I then carefully threaded the tap into the broken shell until it was snug. I found a wood dowel that would fit down the bore and I gently tapped on it with a hammer, and shazamm! the broken shell and tap came falling out