In its application to the Treasury Department, actuaries say the fund will be insolvent by April 2026, and is asking for the authorization to commence benefit suspensions by December 1, 2016.

The Multiemployer Pension Reform Act of 2014 created a new funding designation, "critical and declining," for plans expected to be insolvent in 15 years.

Those plans can apply to the Treasury Department for the right to reduce promised benefits to 110 percent of the benefits guaranteed by the Pension Benefit Guaranty Corp., which insures a maximum of about $13,000 a year.

Read: Moody's warns multiemployer pension sponsors of credit implications

Union members have the right to vote proposed cuts down, but Treasury can override that vote if the plan's inevitable insolvency is deemed to be systemically consequential to the PBGC's balance sheet.

Teamsters Central States

The Teamsters Central States pension plan was the first to file its application to reduce benefits. That plan reportedly has $18 billion in assets, pays $2.8 billion annual obligations, and is only taking in $700 million in annual contributions. It as obligations to more than 400,000 participants.

The Central States plan is the furthest along the application process. This week, Treasury extended the comment period for the process for a second time. Treasury has received well over 2,000 comments so far.

Teamsters Local 469

The Teamsters Local 469 Pension Plan, which is expected to be insolvent by 2029, has also filed its application for reductions. That New Jersey-based plan only has 128 active participants out 1,781 total participants.

In its application to Treasury, the Teamsters Local 469 plan is proposing benefit suspensions begin on October 1, 2016.

More plans are likely to file applications for benefit reductions in the foreseeable future.

The Boston College Center for Retirement Research has complied a non-definitive list of 100 pension funds that may qualify for pension cuts.

Will United Mine Workers 1974 be next?

The second biggest plan on that list, in terms of total participants, is the United Mine Workers of America 1974 Pension Plan, which has 115,120 total participants, and 9.7 inactive participants for every contributing active member.

In a recent Senate Finance Committee hearing examining retirement policy for private sector, non-union workers, several lawmakers to the opportunity to raise the plight facing multiemployer plans, and specifically the question of mineworkers' pension security.

Sen. Ron Wyden, D-Oregon, the Committee's ranking member, called the Multiemployer Pension Reform Act a "bad law," and the funding issues facing multiemployer plans a "public policy emergency."

"This needs to be solved soon," said Wyden, who said Congress needs to enact legislation as soon as possible to help those coal miners facing the prospect of pension reductions.