WASHINGTON — The Supreme Court handed organized labor a major victory on Tuesday, deadlocking 4 to 4 in a case that had threatened to cripple the ability of public-sector unions to collect fees from workers who chose not to join and did not want to pay for the unions’ collective bargaining activities.

It was the starkest illustration yet of how the sudden death of Justice Antonin Scalia last month has blocked the power of the court’s four remaining conservatives to move the law to the right.

A ruling allowing workers to refuse to pay the fees would have been the culmination of a decades-long campaign by a group of prominent conservative foundations aimed at weakening unions that represent teachers and other public employees. Tuesday’s deadlock denied them that victory, but it set no precedent and left the door open for further challenges once the Supreme Court is back at full strength.

When the case was argued in January, the court’s conservative majority seemed ready to say that forcing public workers to support unions they had declined to join violates the First Amendment. Justice Scalia’s questions were consistently hostile to the unions.