Originally Published: 15 JUN 22 10:57 ET

Updated: 15 JUN 22 12:15 ET

By Ariane de Vogue, Tierney Sneed, Priscilla Alvarez and Chandelis Duster, CNN

(CNN) -- The Supreme Court dismissed an appeal Wednesday brought by a group of Republican-led states seeking to intervene in a case challenging the Trump-era "public charge" immigration policy, a version of which the Biden administration has abandoned.

The case did not center on the legality of the rule but instead whether the Biden administration followed proper procedures when it set out to revoke the rule and dismiss pending legal challenges.

The Trump-era policy -- an expansion of the so-called "public charge" rule -- made it more difficult for immigrants to obtain legal status if they use certain public benefits, such as Medicaid, food stamps and housing vouchers.

Wednesday's order is a blow to conservative states that had asked the court step in to reinvigorate legal challenges.

Chief Justice John Roberts wrote a concurrence joined by Justices Clarence Thomas, Samuel Alito and Neil Gorsuch, to explain their votes to dismiss the challenge.

Roberts expressed frustration with the Biden administration for sidestepping certain procedures for reversing the Trump policy. He said the maneuvers raised "a host of important questions" for future disputes.

Nevertheless, he said it had "become clear that this mare's nest could stand in the way of our reaching the question presented" in the case, and therefore agreed that the challenge should be dismissed.

"If the justices had allowed these states to continue to defend the Trump-era policy, that would've set a remarkable precedent for other states to follow at the end of both this presidency and future ones," said Steve Vladeck, CNN Supreme Court analyst and professor at the University of Texas School of Law.

"Although the court did not specifically reject the states' effort, its summary, procedural ruling leaves intact the lower court ruling that did -- a precedent that will matter going forward."

The Trump rule triggered a ferocious attack from immigration rights groups and others who ultimately brought challenges in five separate courts. One judge, in the Northern District of Illinois, issued an injunction blocking the rule nationwide in November 2020. The Trump administration asked the Supreme Court to hear the dispute, and the court agreed to do so in February 2021.

Upon taking office, however, President Joe Biden ordered a review of the prior administration's rule, and ultimately declined to defend it in court. In March, the administration sought to dismiss the remaining pending challenges, leaving in place the nationwide injunction issued by the one federal judge.

The administration removed the rule from the books and said it would ultimately issue a new regulatory definition of "public charge."

The justices took the case off of its calendar.

But Republican-led states said that although new administrations often change positions in pending litigation, the way the Biden administration went about ending the rule in the case at hand was legally questionable and in violation of the Administrative Procedure Act, a law that governs how federal agencies roll out regulations. They argued that the Biden administration's "novel strategy" not only "obliterated" the Trump public charge rule, but it also deprived the states' chances to protect their interests by defending the rule.

The states, led by Arizona, asked to intervene in one case before the 9th US Circuit Court of Appeals to defend the rule, noting that the rule would impact them by more than $1 billion a year. But their request was denied.

The Republican-led states ultimately brought their challenge to the Supreme Court.

Arizona Attorney General Mark Brnovich urged the justices to step in "not just for Arizona, but also to ensure this case does not become a blueprint for evading the APA in the future" calling it an "unprecedented legal maneuver."

"If you allow the actions of the Department of Justice to stand in this case, it sets a dangerous precedent for future administrations to essentially do an end-run around the APA," he said.

The Biden administration countered that the states did not have the legal right to step in, particularly because the lower court's injunction in the 9th Circuit case that they are challenging never applied directly to them. In addition, the administration said that during the year that the rule was in effect, it only affected about five of the approximately 50,000 adjustment of status application cases.

Principal Deputy Solicitor General Brian Fletcher said that the states "do not have a legally protectable interest" in preserving such a "negligible" effect.

The "public charge" provision dates back at least to the Immigration Act of 1882. Federal lawmakers at the time wanted to make sure that immigrants would be able to take care of themselves and not end up being a public burden.

Under current regulations put in place in 1996, the term is defined as someone who is "primarily dependent" on government assistance, meaning it supplies more than half their income.

But it only counted cash benefits, such as Temporary Assistance for Needy Families or Supplemental Security Income from Social Security. The Trump administration's rule widened the definition of who is expected to be dependent on the government by including more benefit programs.

The Trump administration's policy made national headlines when then-acting Director of US Citizenship and Immigration Services Ken Cuccinelli, in his defense of the rule, revised the iconic poem on the Statue of Liberty's pedestal, saying: "Give me your tired and your poor who can stand on their own two feet and who will not become a public charge."

Advocates and several states that opposed the rule said the changes would penalize immigrants who rely on temporary assistance from the government and impose costs on the states.

This story has been updated with additional details.