Among the misunderstandings
When Sears applied to stop paying INTO the pension plan due to bankruptcy, news  reports were that pension chequess FROM the pension plan were cut off. I don't think that was true but it was not clear from the news reports.

Underfunding is usually a bit of an exaggeration since a plan is underfunded if it does not have enough to cover the pension with all assets invested in bonds. In reality with half or more invested in equities it may be fine. 

Almost every balanced portfolio would effectively be underfunded by this calculation as bonds will deliver less than the expected balanced amount.

When a company goes broke, I understand the pension assets must be converted to 100% fixed income which at today's low interest rates is almost certain to make the problem FAR worse.