You can also try these two places. They appear to be part of a federally funded housing thing. (Section 8?? http://www.gosection8.com/what-is-section8.aspx)
I think they base your rent on your income, not sure what they do if that income is 0
Elmira HA
Type: Low-Rent, Code: NY030
737-D Reservoir St.
Elmira, NY 14905
Phone: (607) 737-7100 Fax: (607) 737-7137
Elmira Heights, Village
Type: Section 8, Code: NY432 Rent help, housing aid, and Section 8
215 Elmwood Ave.
Elmira Heights, New York 14903
Phone: (607) 734-1531 Fax: (607) 734-1607