A theoretical I’d just as soon avoid:
A horrible thought just occurred to me: What if Hillary asks Obama to be her VP?
— (((Taxpayer1234))) (@Taxpayers1234) June 15, 2016
There is some argument as to whether she could. See the 12th Amendment, last sentence:
But no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States.
Once he completes his second term, Barack Obama would presumably be “constitutionally ineligible,” per the 22nd Amendment, and therefore could not serve as Vice President, though an amusing argument otherwise can be made.
And there’s a nightmare scenario: A Clinton/Obama ticket is elected, and some nimrod manages to penetrate security and ventilate Her Majesty’s jacket. She dies, the Supremes rule that Barack can’t come back to the White House, and the Presidency devolves upon — the Speaker of the House. What you think of this may depend on whether you think Paul Ryan will be replaced next year.