If the abuser has been convicted of a crime, can s/he legally keep or buy a gun?
Under federal law, if the abuser has been convicted of any felony or of a domestic violence misdemeanor, s/he cannot legally have or buy a gun unless an exception applies (see the "note" below).1 In addition, it is also illegal to have or buy a gun if the abuser is a “fugitive from justice,” which means s/he has fled any state to avoid being prosecuted or to avoid testifying in any criminal proceeding.2
Note: An abuser who works for a government organization (such as a police officer or military servicemember) may still be allowed to possess a work-issued firearm even if s/he was convicted of a felony, is a fugitive from justice, or if s/he has an order of protection issued against him/her . Please see The abuser uses a gun for his/her job. Does the law still apply? for more information.
1 18 USC § 922(g)(1), (g)(9)
2 18 USC § 922(g)(2)