No, if he is not eligible, then he was not the President. We didn't have one. Unless you like the idea of setting that precedent.
Odds are pretty good he didn't win that second election either.
He deserves neither SS protection, nor financial benefits, but rather court, lawsuits and at the very least, long term imprisonment.
Remember the video that came out just after Nov. 8th, “Who’s Laughing Now?” Part of it showed a smirking smirking Obama saying about Trump, “You’ll never be president.” then dropping his e-device. I’ll be honest. I’d like to see that smug expression wiped off his arrogant face.
As a matter of process, the federal government can't operate that way.
It must assume the president is the President, and the congress is the Congress, and the laws enacted by the same are valid.
If, in the future, it's found that some aspect of the ruling order was legally invalid, e.g., the president wasn't eligible, then the outcome must depend upon the opinions of the sitting congress.
Of course, there are hard cases. E.g., a Supreme Court justice confirmed by one vote. But one of his votes turns out have stolen his senatorial election. What is to be done?
Answer: He's Mr Justice Whomever. Unless a majority of the House and two thirds of the Senate ...
And that's how the cookie crumbles.
Obama also has arranged for his MIL to have a lifetime pension of $160,000 a year because ‘she was the caretaker of her grandkids’ while she lived in the White House.
That can get flushed also.