PATH Fairness Act of 2019 This bill reauthorizes through FY2024 and revises the Projects for Assistance in Transition from Homelessness. The program provides services to individuals who (1) are suffering from serious mental illness, or are suffering from serious mental illness and from substance abuse; and (2) are homeless or at imminent risk of becoming homeless. The minimum allotment of program funding for each state and territory is increased on the condition that appropriations are sufficient to provide the minimum allotment to all states and territories.