Would they promote Tim Kaine to the top spot? In theory, the Vice Presidential candidate is someone who is also qualified to be President, and able to step right into the job in the event of unforeseen circumstances such as the death or resignation of the President. This, however, would infuriate Bernie’s supporters (even though he is no longer a Democrat.) If Hillary is removed from the ticket against her will, regardless of her health, many of her supporters will stay home.
All this speculation might have been relevant a few weeks or months ago.
Should Hillary drop dead today, Dems would probably leave the ballot as is, meaning a win would wind up with President Kaine. Why? Replacing Hill at this late date would raise too many questions that would have to be resolved state by state and in Congress, neither of which Dems could count on.