Rainbow Demon is talking about the Dardic "tround" system:
It used the shell as part of the chamber. My setup uses factory 9mm ammo and feeds shells in from the rear, not the side.
The closest thing to my setup is an experimental Nazi 20mm cannon captured late in WW2 and never put into service, the Mauser MG 213:
As you can see, it did mechanical insertion (in two stages) and mechanical extraction (one stage). In my case I'm doing spring-loaded insertion, gas-powered extraction...and of course mine spins the other way
. The German design was belt-fed, electrically spun and fired full-auto. Mine...well, IF I were to rig another gas line for cocking it would indeed go full-auto! I suspect that with 9mm+P+ ammo there might be enough gas pressure available to power a cocking stroke.
Variants of this were later used by various allied countries in 20mm and 30mm flavors. In the US we used the design in the F86 Saberjet of the Korean War era.
At least some are still in use.
So far as I know this feed cycle or anything remotely like it has never been used in a handgun, shotgun or personal rifle before now. It was certainly possible as early as around 1896: John Browning was already doing experimental gas-cocked leverguns, and the rimless ammo that makes this practical in something the size of my gun has existed at least since the Broomhandle Mauser of 1896.