The Bureau of Alcohol, Tobacco, Firearms and Explosives has issued several letters regarding the legality of the SB Tactical Pistol Stabilizing Brace, including this one from 2012.
The bottom line: The ATF has stated that the SB Tactical Pistol Stabilizing Brace is legal to own, legal to purchase and legal to install on a pistol. The ATF has consistently stated that a pistol with a Pistol Stabilizing Brace attached remains a pistol under the Gun Control Act when used as designed.
EXCERPT (2012 ATF letter):
“Based on our evaluation, FTB finds that the submitted forearm brace, when attached to a firearm, does not convert that weapon to be fired from the shoulder and would not alter the classification of a pistol or other firearm. While a firearm so equipped would still be regulated by the Gun Control Act, 18 U.S.C. § 921(a)(3), such a firearm would not be subject to NFA controls.”