Housing Homeless Veterans Act of 201 9 This bill establishes certain priorities for funding distributed under the Veterans Affairs Supportive Housing (VASH) program and requires the reallocation of certain unused funds under the program. Specifically, the Department of Housing and Urban Development (HUD), in making VASH program funds available among public housing agencies (PHAs) for rental voucher assistance for homeless veterans who have chronic mental illnesses or chronic substance-use disorders, must give priority to PHAs that (1) serve areas that have the highest numbers of homeless veterans, (2) have fully utilized their available HUD-VASH funds for the preceding fiscal year, and (2) have demonstrated need for such incremental assistance. Additionally, HUD must (1) recapture certain unused HUD-VASH assistance from PHAs in jurisdictions with decreasing homeless populations, and (2) reallocate the recaptured amounts to PHAs that have used their entire allocations of HUD-VASH assistance.