Andrew, Pioneer Arms PPS 43 is legally classified by BATF as a pistol. The folding stock is fixed in place and is non-functional. Otherwise it would be considered an SBR. This firearm is an ATF approved pistol. The stock has no function and is permanently fixed in its folded position.

Andrew, this Fixed in position stock is perfectly legal on this Handgun/Pistol Sir. Cheers and stay safe!

Its a pistol with a Faux stock From the Pioneer website see *****Pioneer Arms has redesigned this historical firearm to shoot from a closed bolt position. The safety is located at the front of the trigger guard. The receiver and barrel shroud are made from stamped steel. The rear sight is an L-shaped flip type and is marked for 100 and 200 meters distance. The front sight is a fixed blade. The barrel is equipped with a simple muzzle brake. This firearm is an ATF approved pistol. *******The stock has no function and is permanently fixed in its folded closed position. pioneer-pac.com/pps43-c-pistol,prp1,7,2

James is correct, seems really odd they didn't just take the stock off, or add a brace instead.
But yeah stock doesn't fold down,copy and paste from pioneer arms website "
The stock has no function and is permanently fixed in its folded closed position.
"
-------------' full details here
pioneer-pac.com/pps43-c-pistol,prp1,7,2