Although several states have their own branch departments for this service, at the federal level what you are referring to is actually the Administration for Children and Families. It is a branch of the US Department of Health and Human Services. According to the DHH website, the ACF vision, mission, and goals include providing funding, services, and other public resources to help create families and communities that are “resilient, safe, healthy, and economically secure.” The Administration executes this vision via the work a number of different bureaus and offices.
The kinds of services the Administration offers depend on the kinds of crises that families find themselves in. For example, low-income households often face crisis in meeting their basic financial needs, purchasing groceries and medicine, and maintaining their rent payments. The Administration’s Office of Community Services offers a number of different programs, such as the Community Services Block Grant and the Low Income Home Energy Assistance Program, which provide money to state organizations so that they may assist low-income households meet their basic material and energy needs: https://www.acf.hhs.gov/sites/default/files/ocs/factsheets_ocs.pdf.
The Office of Family Assistance also has large tracts of money available to assist low-income families with children. Through their Temporary Assistance for Needy Families program, this Office disstributes 16.6 billion dollars annually to state governments for the purposes of family assistance. Other low-income households may be eligible for a Health Profession Opportunity Grant. This grant provides education and training to individuals from low-income families in selected health-profession fields that are expected to face labor shortages or be in high demand. Such training opportunities guarantee stable career opportunities for individuals to settle their household finances and enter the workforce: https://www.acf.hhs.gov/sites/default/files/ofa/factsheets_ofa.pdf.
Probably the division of the Administration most germane to this question is the Office of Human Services, Emergency Preparedness & Response. If a community as a whole is in crisis, say because of the coronavirus outbreak, this is the Office that will do the most immediate work to rectify the situation. This Office works in conjunction with administrators of the ten Health and Human Services regions to prepare and execute efforts to stem the worst consequences of emergency situations. As the Office’s mission statement reads:
The Office of Human Services Emergency Preparedness and Response (OHSEPR) promotes the resilience of vulnerable individuals, children, families and communities impacted by disasters and public health emergencies, and provides expertise in human services preparedness, response and recovery through policy, planning, operations and partnerships.
The coronavirus outbreak would be an example of such a disaster covered under the mission statement. The Office does not have any programs of its own. Rather, it coordinates with other Offices and Bureaus of the Administration in order to ensure the continuity of service delivery and to meet surge requirements for disaster victims. In addition to coordinating with other Administration branches, this Office provides technical assistance, administrative liaisons, and subject-matter experts to sites in need of immediate response: https://www.acf.hhs.gov/sites/default/files/assets/factsheets_ohsepr.pdf.
To reiterate, the Administration for Children and Families falls under the jurisdiction of the US Department of Health and Human Services, so all of its funding comes from the funding available to that Department.