The median funding level of the plans was 86 percent at the end of 2013, a vast improvement from the 68 percent median in the wake of the 2008 financial crisis.

By 2013, 57 percent of plans were designated to be in the "green zone" status, the metric established under the Pension Protection Act of 2016 for the best-funded plans. Plans in the green zone have a funded status greater than 80 percent. Only 34 percent of plans held green zone status in 2009.

Still, challenges remain going forward even for the better-funded plans.

In 2004, the median ratio of active participants to retirees in all multiemployer plans was one-to-one. By 2013, the median ratio had shifted dramatically, to six active participants for every 10 retirees.

"The higher investment returns and increased funding levels of plans are good signs, but plans on the whole are becoming more mature," said Jason Russell, a consultant with Horizon Actuarial Services. "When you look at demographics and net cash flows, it's clear that plans are aging and tilting toward more inactive versus active members."

That demographic sea change will force trustees to reevaluate funding and investment strategies, as it will be difficult to maintain and improve funding levels simply by increasing contributions, explained Russell in a statement.

By the end of 2013, there were also 1,132 multiemployer defined contribution plans, 80 percent of which were offered in tandem with defined benefit plans.

That DC plans held $120 billion in assets and covered more than 3.7 million participants, the study said.