Fostering Stable Housing Opportunities Act of 2019 This bill gives the highest preference under certain federally assisted housing programs to youths who are aging out of foster care, provided that the youths comply with specified educational, occupational, or training requirements. The bill provides exceptions to these requirements for certain youths, including those who are caregivers for young children or who have certain medical conditions. Current law already gives preference under certain federally assisted housing programs to youths who are aging out of foster care.