I don't think that Hillary would or should selected Bill as VP.
but he would be constitutionally ineligible from succeeding her in the event of death/resignation - that would go to the Speaker.
That's not clear either. The text of the amendment says "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."
The last sentence of the Twelfth Amendment states that "no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States." If you are constitutionally ineligible to be elected President because you've already been elected twice, you can't be elected Vice President, either.
I believe Bill is eligible to serve as president again. He just can't be
elected president again. The 22nd Amendment talks about being elected president, not serving as president. Thus, I do think he could be elected VP, and become president via the death or resignation of the sitting president.
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