From The Federalist:

Kaine’s proposed law, entitled the “Responsible Transfer of Firearms Act,” places a criminal federal liability on anyone who transfers a firearm to an individual prohibited from possessing one by federal law, according to a fact sheet provided by Kaine’s office. Under current law, only federal firearms licensees (FFLs) are criminally liable if they sell a gun to a prohibited individual. Kaine’s law would extend that criminal liability to private individuals as well.