The only example of this I'm aware of was Joe Lieberman running for Vice-President and for re-election to the Senate in 2000. As I recall, there was some unusual set of laws in Connecticut that allowed him to do this.
Kind of lame, really; he was more or less conceding that his ticket couldn't win the Presidential race, and needed a backup plan.
That's because Bush had a small to sizeable lead in almost all polls throughout much of the campaign. I remember watching NBC News just about every night during the height of the campaign, and a picture of both Bush and Gore would come on the screen, and one would go to the top of the screen, the other to the bottom. I remember seeing it many times, and only once remember Gore going to the top.
As we know today, those polls were correct.
