No such thing, if one wants to observe the Constitution of the United States, as an illegal gun. Guns may be possessed illegally, such a felon whose punishment included the loss of RKBA, but for the otherwise law abiding citizen, there is no such thing as an illegal gun, knife or other arm.
touche’!!!
You can certainly make an illegal gun. Saw off a shotgun barrel below the specified length. Build a T/C Encore with a rifle buttstock and a 15" pistol barrel. That's a short barreled rifle by ATF definition. It requires a special application, a $200 tax stamp and SBR engraving on the frame. I could go on, but the point is that it is possible to create a gun that is illegal. That was a centerpiece of the Emerson decision. The sawed off shotgun was deemed not to be a "military" weapon. The case was goofy and wrong. It continues to haunt us.