Under federal law, if the abuser has been convicted of a felony or a domestic violence misdemeanor, s/he cannot have or buy a gun.¹  If you're not sure if the abuser has been convicted of a domestic violence misdemeanor, see What crimes are considered domestic violence misdemeanors?

In addition, KS state law says that is illegal for people convicted of the following crimes to own or possess a gun:

• a person who has been convicted of a "person felony," which are various drug crimes (listed in sections K.S.A. 21-36a01 through 21-36a17 of the law); or convicted of any violation of the uniform controlled substances act prior to July 1, 2009,
• someone who was a "juvenile offender" of an act which comes under the "person felony" crimes or uniform controlled substances act prior to July 1, 2009, AND was in possession of a firearm when s/he committed the crime; or
• someone who was convicted of certain felonies within the past 5 or 10 years, or has been released from imprisonment for a felony; or someone who was a juvenile offender for these felonies AND had a gun at the time of the crime.²

¹ 18 USC 922 (g) (9)
² Kan. Stat. Ann. §21-6304(a)