A background check would have stopped the sale in its tracks and gotten the perp immediately locked up and facing charges of a felon attempting to purchase a firearm.
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The part you mentioned in bold very rarely happens.
The FBI, in reviewing instant background checks for firearm purchases, detected 112,000 lie-and-try crimes in fiscal 2017 alone, and federal investigators had names and addresses on the filled-out forms. How many were prosecuted? Twelve, according to a recent Government Accountability Office report.
https://www.usatoday.com/story/opin...-12-prosecuted-editorials-debates/1288699002/