Under the proposal that the plan filed with the Treasury Department late last month and shared with members on Tuesday, more than half the plan’s participants would see no reduction in their benefits; about 45 percent would see their retirement benefits reduced by up to 19 percent of what they have been promised; and a little under 2 percent would have their benefits cut by 20 to 40 percent. Benefits would not be cut for retirees over 80, and cuts would be reduced for those over 75.

If approved, the cuts would go into effect next year.

Several musicians expressed concern about the proposed cuts. Adam Krauthamer, the president of the union’s largest local, Local 802 in New York, said in an email to The New York Times that it was “a tough day for unionism, for the A.F.M. and for my fellow musicians across the country.”

The executive board of Local 802 wrote in an email to its members that many musicians “will be severely impacted by the impending cuts.” Officials at the local pledged to scrutinize the proposed cuts and the application process; work to help Broadway musicians implement a new 401(k) plan to help them prepare for retirement; and push for more accountability from the pension fund and the board of trustees that oversees it.

The American Federation of Musicians, both nationally and among its local chapters, has been pushing for federal legislation to help address the growing national problem of underfunded multiemployer pension plans. But there have been few signs of action in Washington.

The underfunded musicians’ plan and the prospect of benefit cuts have roiled the union in recent years. Mr. Krauthamer was an insurgent candidate who was elected president of Local 802 in 2018 in a major upset that was driven largely by concerns about the plan. Some musicians have sued the plan’s trustees, claiming mismanagement of the fund, which the trustees have denied. Many rank and file musicians are becoming activists when it comes to their pensions.