Emergency Family Stabilization Act This bill establishes a competitive grant program within the Administration for Children and Families (ACF) for family stabilization agencies to provide emergency relief to children, youth, and families experiencing homelessness. These agencies include current ACF grantees or subgrantees, Indian tribes, tribal organizations, Native Hawaiian organizations, and other organizations with expertise providing direct services to those experiencing homelessness. Recipients may use grant funds for, among other purposes, personnel costs, personal protective equipment, and other supplies to mitigate the spread of COVID-19 (i.e., coronavirus disease 2019), as well as payments for security deposits and other housing-related needs. Additionally, the ACF must award the grants based on factors including the need for the services in the area served by the agency and specified allocation and prioritization requirements.