Sorry. Doesn't work that way.
We retired a CEO/director a year after his contract was expired. Even retroactively put him on voluntary leave with full benefits for a while before his contract expired. He got back pay, but no SSA. The Federal government has its only legal reality; private contractors can have a different legal reality; and neither have to be all that incredibly close to what actually happened.
That wouldn't have been easily possible when I worked in a warehouse. Things weren't by contract like that, they were by formula. You fit in a slot or you don't. It's a limited world, but it's handy for most employers and employees. That world can be expanded: If you are the subject of discrimination and fired when you're nearly at retirement, part of the settlement can be retirement and back pay for the time you were "on leave." It's not just for the rich: It's for those who have leverage, legal or financial. It doesn't have to go through a court, either. It just has to be agreed upon by both sides. It helps if there's nothing around to violate the legal fiction: If you find that so-and-so "retired" but was responsible for all kinds of decisions, the fiction's hard to maintain. If he wasn't around, or just sort of was an observer and didn't decide much in his non-job, it's easier to maintain the fiction. Well, I call it "legal fiction," but legally it's fact.
Had a student transfer into my class retroactively having passed all her tests. And a public school allows you to "fix" failed classes by doing additional work, so that you may fail English in March but in May you can have passed English in March. It required a fair amount of effort on the part of the school to make this happen--space, equipment, staff, planning time. But it helped some kids graduate. (Hey, they can even fail a required course, graduate with the 'minimum plan', and then make up course work that they failed and find that really they graduated with the 'recommended' plan, the one colleges like.)