There was never a production trench gun in the US based on the Browning. In fact there weren't any Browning riot guns made in WW2 for the US military either- the Browning factory was in Belgium, and got overrun by the Germans. There was no way they could manufacture shotguns for the US government after that. FN had licensed production of the Browning design to Remington in the early 1900s due to tariffs, so we had far more Remington Model 11s than early Brownings here in the US.
Browning produced what were called 'messenger guns' in the early 1900s, short barreled security type shotguns we would call riot guns today. That was the formal designation in their 1903 catalog (Grade No. 0, Messenger Gun). At the time, short barreled shotguns of all types- double barrels, pumps or semiautos- were often called messenger guns. They were intended for law enforcement, express company or bank guards, railway police etc. as fighting shotguns. So the history of Browning fighting shotguns goes way back.
There were Remington Model 11 riot guns used by the US military, Remington Sportsman riot guns (the 3-shot magazine Model 11, basically) and Savage 720 riot guns, but no Brownings. Browning autos were popular among partisans in Europe who fought the Germans, but as the war wore on ammunition dried up and the shotguns were abandoned for captured German military weapons, or the weapons supplied by the Allies who were supporting and guiding the partisan efforts (OSS, SOE, Jedburghs etc. (
http://ossinitaly.org/index.html ,
http://en.wikipedia.org/wiki/Office_...tegic_Services etc.)
And no one never really figured a way to make trench guns out of the long recoil type action shotguns. There were a few experiments and prototypes, but never a production model. Remington built a Model 11 trench gun prototype for WW1 in 1918 that had a sleeve or jacket around the barrel to which the bayonet lug was attached. The barrel recoiled inside the jacket which surrounded the barrel. If you think about how the long recoil action works, you'll understand why putting a bayonet on the barrel itself and sticking something with it was a Bad Idea. The barrel jacket idea worked, but it was never produced.
A number of US outlaws in the Depression era liked cut-down semiauto shotguns, John Dillinger, Clyde Barrow, and Bonnie Parker among them. They chopped the guns off as short as possible and didn't care how much they battered themselves- they tended not to keep guns very long anyway. rbernie is correct in his advice above about not taking too much off the barrel. And how much you can cut down the stock is limited by the bolt return spring tube that goes about halfway back. Here's a pic of Bonnie funnin' around with Clyde, with a cut-down Remington-
http://www.accuracyproject.org/cbe-Barrow,Clyde.html . They liked having their pictures taken.
There were a good many sporting type shotguns used by the military in WW2 as training guns to teach budding aerial gunners (waist and turret gunners on heavy bombers) how to hit moving targets. And there were sporting guns owned by installation recreation activities used for skeet and trap shooting. Those guns were all military owned, and military marked. I'm told there were some Brownings in that number, I don't know if they were WW2 era or not.
Brownings were used by the British in Malaya in the guerrilla war there, which also saw the deployment of the Remington 870 in its first debut as a fighting shotgun not long after its introduction. The Rhodesians also used the Browning in their fight against communist guerrillas. That long-magazine Browning 'jungle gun' mentioned above as being listed at the auction site was prototyped in the 1960s, and at least a few of them saw production. It's an interesting variation, and I find it sort of surprising it wasn't kept in production.
Get your hands on a copy of Swearengen's
The world's Fighting Shotguns for pictures of most of the things mentioned above... or see Canfield's book-
http://www.brucecanfield.com/uscombatshotguns.html .
hth,
lpl