Helping Homeless Veterans Act of 2019 This bill permanently extends the following Department of Veterans Affairs programs and services: homeless veterans reintegration programs, referral and counseling services for veterans at risk of homelessness who are transitioning from certain institutions (including penal institutions), financial assistance for supportive services for very low-income veteran families in permanent housing, a grant program for homeless veterans with special needs, treatment and rehabilitation for seriously mentally ill and homeless veterans, housing assistance for homeless veterans, and the Advisory Committee on Homeless Veterans.