Grandfamilies Act of 2019 This bill expands access to specified programs for children living with grandparents or other family members who are not their legal guardian. Specifically, the bill provides that a child of a relative eligible for Old-Age and Survivors Insurance benefits is eligible for such benefit payments if that child (1) began living with such relative before age 18, (2) receives at least 50% of their support from such relative, and (3) has lived with such relative pursuant to a court order for at least 12 months. Additionally, the bill revises the Temporary Assistance for Needy Families (TANF) eligibility requirements for children living with specified caretaker relatives. First, the bill lessens the requirement for TANF applicants to assign their rights to child support when such assignment may impact the likelihood of reunifying the child with their noncustodial parent, such as where the noncustodial parent is working to gain financial stability so they may reunify with their child. Further, when a child, but not the caretaker relative, receives TANF benefits (i.e., child-only cases), or if the caretaker relative is 55 or older, the bill (1) excludes such caretaker’s income from that child’s eligibility determination, (2) removes the 5-year cap on assistance, and (3) exempts such caretaker relatives from TANF work requirements. The bill also (1) encourages states to enact temporary guardianship laws, (2) establishes the National Technical Assistance Center on Grandfamilies, and (3) provides grants for state plans to support caretaker relatives.