PBGC only insures some part of a pension, has many exclusions, and is definitely not "funded" enough itself to protect against the number of pension funds that are running out of funds.
Note that certain non-profits are not obligated to be federally insured. The most notable example of this is hospital staff, as a significant number of hospitals are run by religious organizations.
httpss://en.m.wikipedia.org/wiki/Pension_Benefit_Guaranty_Corporation