Possession of a firearm, under 18 U.S.C. 922(g)(5), should not be considered to be a crime involving moral turpitude. Since possessing a firearm is not inherently evil and not malum prohibitum, the fact of being unlawfully undocumented when doing so should not make it a crime of moral turpitude. See Matter of Hernandez-Casillas, 20 I&N Dec. 262 (BIA 1990) (possessing a sawed-off shotgun not a crime of moral turpitude). See also Matter of Gabryelski, 20 I&N Dec. 750 (1993):

[W]e point out that while the respondent's conviction for possession of a firearm establishes his deportability under section 241(a)(2)(C) of the Act, see Matter of Chow, Interim Decision 3199 (BIA 1993), it does not render him inadmissible for purposes of section 245 adjustment, as there is no corresponding exclusion ground. In Matter of Rainford, supra, the Board specifically held that a conviction for criminal possession of weapon did not preclude a finding of admissibility in connection with an application for adjustment of status under section 245 of the Act, because it is not a ground of excludability.

(Ibid.) Since it is not a ground of inadmissibility, it is not a crime involving moral turpitude. Thanks to Jonathan Moore.