Promoting Resident Opportunities and Self-Sufficiency Act This bill provides for the continuation of assistance for public housing residents through certain service programs. Specifically, the bill allows residents of properties that have been converted through the Rental Assistance Demonstration Program to project-based subsidy contracts to continue to receive assistance through (1) the Resident Opportunities and Self-Sufficiency grant program, (2) the Jobs Plus Initiative program, and (3) certain congregate housing services.