Will the abuser go to jail for having a gun when s/he isn't supposed to?
New York state law says that any violation of the New York laws regarding gun licenses is a Class A misdemeanor (the highest level of misdemeanor) that can be punished by a fine of up to $1,000, jail time for up to one year, or both.1
In addition, if someone is convicted of a felony or a "serious offense," the judge is required to order the defendant to immediately surrender all firearms, rifles, and shotguns that s/he owns or that are in his/her possession. The judge will then instruct the local police to immediately notify the court when the defendant has surrendered his/her firearms, rifles and shotguns.2
Note: Generally, the abuser does not have to have knowledge of the law in order to be arrested (and convicted) for violating the law. If the abuser has a gun or buys a gun in violation of the law, the abuser can be arrested and convicted, whether or not the abuser knows s/he was in violation of the law. "Ignorance of the law" is no excuse or defense.3
1 NY Penal Law §§ 400.00(15), 80.05(1), 70.15(1)
2 NY CPL § 370.25(1), (2)
3 See, for example, United States v. Denis, 297 F.3d. 25 (1st Cir. 2002); United States v. Lippman, 369 F. 3d 1039 (8th Cir. 2004); United States v. Henson, 55 F. Supp. 2d 528 (S.D. W.V. 1999).