It's called an "AOW" or Any Other Weapon. It is NFA but it's not quite a "short barreled shotgun".
SBS will have a stock originally where the AOW doesn't. Through some bizarre ATF interpretations that's how it worked out.
The nice thing about AOWs is the NFA tax stamp is only 5 bucks rather than 200 for an SBS.
Can I take an old shotgun and do this to it?
This is where it gets weirder. If your shotgun originally had a stock you cannot make an AOW out of it, only an SBS.
You could make a shotgun look exactly like the Serbu certainly but you will need a $200 stamp instead of a $5 stamp.
If you take something like a Mossberg Cruiser and whack the barrel off then you can make an AOW since the Cruiser didn't have a stock as a Title I firearm. In fact the Serbu is just a Mossberg Cruiser anyway I think.
The Serbu doesn't "fit' into the SBS definition because it's actually a "smooth bore handgunl" rather than a shotgun
Clear as mud huh......then there are any state laws where you live that might impact your ability to own one.
Just for info, things like pen guns and cane guns are considered AOWs as well.