Assignment of Support Rights
The legal procedure by which a person receiving public assistance agrees to turn over to the State any right to child support, including arrearages, paid by the non-custodial parent in exchange for receipt of a cash assistance grant and other benefits. States can then use a portion of said child support to defray or recoup the public assistance expenditure.
Source: Office of Child Support Enforcement.
When a person that gets public assistance (money from the government) agrees to give the state any child support they get in the future. The person gets money and other benefits from the state. So the state can use part of the child support to pay for the cost of that public assistance.
Source: California Courts.