Homeless veterans can have housing through the HUD-VASH program (Veterans Affairs Supportive Housing

If you’ve served your country (accepted the risk of death), you may qualify for housing apart from other entry points.

The HUD-Veterans Affairs Supportive Housing (HUD-VASH) program combines HUD’s Housing Choice Voucher (HCV) rental assistance for homeless Veterans with case management and clinical services provided by the Department of Veterans Affairs (VA). VA provides these services for participating Veterans at VA medical centers (VAMCs), community-based outreach clinics (CBOCs), through VA contractors, or through other VA designated entities.

The part I find in talking about this is proving homelessness. Good to check current requirements.