"No President-elect has in fact failed to be sworn in. Nevertheless, the rules for what would happen if a President-elect were to be unavailable to be sworn in actually became a part of our law with the adoption of the 20th Amendment in 1933.
This amendment was passed primarily to shorten the length of time between the general election and the beginning of the new administration (inauguration day was moved from March to January).
But it also specified that if, at the time of the inauguration, the President-elect has died, then the Vice-President-elect becomes President"
So if Hillary wins the election and dies before being sworn in, Kaine becomes President
http://teachinghistory.org/history-content/ask-a-historian/20431
Thank-you!