Here's the exact text of the 22nd Amendment:
1: No person shall be elected to the office of the President more than twice, and no person who has held the office of President, or acted as President, for more than two years of a term to which some other person was elected President shall be elected to the office of the President more than once. But this article shall not apply to any person holding the office of President when this article was proposed by the Congress, and shall not prevent any person who may be holding the office of President, or acting as President, during the term within which this article becomes operative from holding the office of President or acting as President during the remainder of such term.
So, you've asked a good question, and in my opinion, he can run for VP and he can serve if the elected President dies in office. He just cannot run for re-election.
Actually, there's another way he could end up president. If he ran for Congress and was selected as Speaker of the House, he'd be third in line, right behind the President and VP.
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This is a question that comes up a lot. It seems to be that one cannot be vice-president once having served teo terms as president, because of the 12th Amendment's stating that one who is ineligible to be president (and having served two terms, he/she would be ineligible) cannot be VP.
Google this and see what Constitutional scholars have to say. That's my take.
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