N.M. Stat. § 53-10-2
Any such club or association may hold and acquire real or personal property by deed, lease or otherwise, in the name of such association by which it is known, and to [may] acquire title to any property by purchase or otherwise for its objects and purposes, which property shall be deemed in law to be held by the said club or association for the use and benefit of the actual and active members thereof composing said association from time to time,[;] and upon the decease of any member, or the termination of any membership therein, the interest of any deceased member, or the interest of any member whose membership is terminated, in the property real or personal of such association shall cease and terminate, without right of succession to the heirs, executors and administrators of such deceased member, or to the creditors or trustee in bankruptcy or assignee of any member whose membership in said association shall be terminated. The interest of any member in the real and personal property of any such club or association shall not be subject to execution as and for his debts or as his individual or special property.
NMS § 53-10-2