Something which, notably, happens on around 1% of all applications, but is prosecuted less than 0.000005% of the time.

From 2008 - 2012 there were 32 million background checks, and 373,900 rejections.

Between FY 2008 and FY 2015, an 8-year period, ATF formally referred 509 NICS denial
cases that included 558 subjects to USAOs for possible prosecution. The USAOs
accepted for consideration of prosecution 254 subjects (or less than 32 subjects per
year) and declined to prosecute 272 subjects.

32 prosecutions a year for an average of 6 million background checks (completed, there is a much larger number for bg checks initiated)