Any idea what it is and why the body less wide closer to the head?
This case looks to have been made in a basic workshop on a lathe.
It was probably made slightly too small and was blown out when fired in a standard 12 gauge chamber.
I agree with Falcon, you can see the tool cutting marks this was done on a lathe that did not have automatic feed.
Is the head end screwed onto the tube part, as there appears to be a joint in the case?