Not Social Security-related, but since it draws a bit on my work on state pension liabilities relative to state debt, this might be of interest. Cato's Chris Edwards runs a simple regression of the share of the state government workforce that is unionized on the state's debt/GDP ratio.
As it turns out, the relationship is pretty significant. Chris has a backstory on how it would play out, although I think it's also possible that a third variable drives both. Worth checking out in any case.