The Trump-era "public charge rule" allowed immigration officials to deny people permanent residency (ie: Green Cards) if it seemed likely they would need public aid, such as Medicaid and food stamps.
Before Trump, only long-term aid counted against green card applicants. Trump's rule changed that so if people used aid in any 12 months in a 3-year period, they could be denied. Using 2 kinds of benefits in a single month counted as 2 months.
The policy was blocked by lawsuits around the country, but a 5-4 Supreme Court vote kept it going while those cases were appealed.
Biden took office and chose not to defend the policy in court. As a result, the Supreme Court and federal courts dismissed any appeals.
Using the decision of the federal court in Illinois, the Biden government canceled the policy. It didn't follow proper procedures, so it has since started that process.
Arizona and 12 other Republican-led states tried defending Trump's rule by filing a motion in a case already before the US Court of Appeals in San Francisco. The case involved 3 lawsuits challenging Trump's public charge rule. The motion was denied by a divided 3-judge panel of the appeals court.
In February, the Supreme Court criticized both the Biden government and the 13 states for how they handled the matter. A key criticism was whether the Biden government had followed the principles of administrative law - which is at the foundation of good governance