If the abuser has been convicted of a crime, can s/he keep or buy a gun?
Arizona state law says that if a person has been convicted of a felony in any state, is currently on probation for a domestic violence offense (as defined by law), has been found "guilty except insane" of a crime, or has been found incompetent by a court pursuant to rule 11, Arizona Rules of Criminal Procedure, and who has not been found competent since that time s/he cannot have or buy a gun.* Federal laws, which apply to all states, also restrict a person's right to have a gun if s/he has been convicted of certain crimes. Go to Federal Gun Laws to get more information.
* A.R.S. § 13-3101(A)(7)(b),(d),(f),(g)