Homeless Veterans Prevention Act of 2019 This bill expands programs, and revises policies, related to veterans who are homeless or at risk of homelessness. Currently, grant recipients under the Department of Veterans Affairs (VA) comprehensive service program for homeless veterans receive per diem payments for services furnished to homeless veterans. The bill provides that furnishing care for a dependent in the care of a homeless veteran (who is receiving services from a grant recipient) may count as a service for which grant recipients may receive per diem payments. The bill requires the VA to enter into partnerships with public or private entities to fund a portion of the legal services such entities provide to homeless veterans and veterans at risk of homelessness, including legal services related to housing, family law, criminal defense, and income support. Under the bill, veterans who are receiving assistance under the Housing Choice Voucher Program are eligible for specified VA dental care. The bill repeals the sunset on the authority of the VA and the Department of Labor to carry out a program of referral and counseling for veterans who are at risk of homelessness and are transitioning from certain institutions (e.g., penal institutions). The bill also extends authorization through FY2020 for the VA to provide financial assistance for supportive services for very low-income veteran families in permanent housing. The Government Accountability Office must complete a study of VA assistance to homeless veterans. Finally, the bill repeals an annual reporting requirement related to VA assistance to homeless veterans.