Anyone who has been convicted of a felony is banned by federal law from ever possessing “any firearm or ammunition." Specifically a person "convicted in any court of a crime punishable by imprisonment for a term exceeding one year" cannot possess any firearm in any location. 18 U.S.C. 922(g)
It is a crime for a felon to attempt to purchase a gun, just as it is a crime for someone to attempt to purchase illegal drugs. Since your claim is that Brady stopped 1.9 criminals from owning firearms there should be 1.9 million arrests, trials and convictions. I have countered that with NUMEROUS sources showing that the reality is...the VAST majority of people 'stopped' are stopped temporarily due to some administrative snafu, failure in paperwork, etc.