2019 BJS results:
"An estimated 287,400 prisoners had possessed a
firearm during their offense. Among these, more than
half (56%) had either stolen it (6%), found it at the
scene of the crime (7%), or obtained it off the street
or from the underground market (43%). Most of
the remainder (25%) had obtained it from a family
member or friend, or as a gift. Seven percent had
purchased it under their own name from a licensed
firearm dealer."
Long story short, most are illegal, stolen or given by a family member. How would strict regulation affect this? I suppose an impact on the "gifted" guns if the person prior was barred from purchasing it but that's speculative.