Stop Arming Felons (SAFe) Act - Amends the Federal criminal code to: (1) deny natural persons the opportunity to seek administrative relief from prohibitions against possessing, shipping, transporting, or receiving firearms or ammunition; (2) prohibit the possession of, or transactions in, firearms by any natural person convicted of a serious drug offense or violent felony, regardless of any expungement of the conviction or restoration of other civil rights; and (3) require publication of additional information about administrative relief granted to any person.