As far as selecting a "successor," I'm not sure how that would happen. A lot of this depends on deadlines in individual states to get candidates on ballots. Most of these deadlines come up in September, if I remember correctly -- so a last-minute change like they did in New Jersey isn't really an option.
IIRC during the summer of 2000 someone on FR came up with Hillary being registered as a presidential candidate. They posted the Fed site showing it. I don't know what effect that would have on state ballots. It would be interesting to know.
It would be a weird situation for one of the major candidates to drop out or croak so late in the game, but presumably the electors could vote for a replacement candidate.