There are several options for affordable housing. Link to a listing of affordable housing complexes in the City limits and you are welcome to call and apply at complexes listed. There are units in these “affordable housing” complexes where the rent is based on a percentage of your income.
The Mesilla Valley Public Housing Authority has public housing units and manages the Section 8 Housing Choice Program. They likely have a long waiting list. Contact Mesilla Valley Public Housing Authority at 575-528-2000. https://www.mvpha.org/
Mesilla Valley Community of Hope provides homeless or near homeless services. Contact them at 575-523-2219 and they are located at 999 W. Amador. http://www.mvcommunityofhope.org/
For home ownership opportunities, the City works with two agencies: Tierra Del Sol Housing Corporation https://tdshc.org/ (575-0541-0477) and Mesilla Valley Habitat for Humanity https://www.lascruceshabitat.org/ (575-525-0475). You can apply with these agencies at any time throughout the year. These two agencies receive funding from the City to build affordable homes and the sales price of the home is reduced by the amount the funding the City has provided for the home.