They own it now, like most of the other unions. If they screw over the union members like some companies, or the government has, there's going to be a lot of bodies to keep Hoffa company.
The truth of the matter is that companies that has such contracts are legally required to have fully funded pension programs (with the exception of public/government employees apparently). Some companies do well at this, others shirk their contract obligations, usually due to malfeasance, and try to weasel their way out of paying (usually because the pension funds were looted/embezzled or mishandled).
If this were your 401K, IRA, SS, or pension fund, those people would be doing prison time. The largest problem right now is with PUBLIC/GOVERNMENT union pension funds.
Private sector unions are a small fraction of the US workforce, less than 10% at the high end, and most of those are trade unions. The public sector unions are the elephant in the room that need to be dealt with.
The only thing that matters are required contributions. A plan that does not require hard cash untouchable contributions then it is just a promise and not a plan. Social Security is public pension plan with all the same issues.