Are the pistol braces illegal to own regardless of whether they are on a gun or not?
No, the ATF cannot regulate accessories. Pistol braces are perfectly legal to own.
HOWEVER, (and there always is a 'however,') if you own a pistol, and that pistol can accept a brace (because it has a carbine style buffer tube, or other adapter), and you have a pistol brace in a box but not on the pistol, you are in what the ATF calls "constructive possession" and are still in possession of what the ATF is calling a Short Barreled Rifle.
Your pistols must not be capable of readily accepting a pistol brace in order to have the brace be just a lump of plastic and velcro.
“Are the pistol braces illegal to own regardless of whether they are on a gun or not?”
You can legally own a brace, like you can own a stock. If just assume a brace is now a stock it makes this all easier to understand.
There is a grey area where if you have the parts to make a short barreled rifle, but don’t have them completely assembled, the ATF may still consider it a short barreled rifle. So taking off the brace, and keeping it in the guns safe next to the gun it came from is going to tempt the ATF to say you are doing something illegal.