So let's just say that Franklin Pierce had tragically perished in the train derailment that killed his son. Even though Pierce was not sworn in, the electoral college vote already occurred, so he was in line to be the next President. That would mean that William Rufus Devane King would be President, as we mentioned earlier. But it would have been a short-lived Presidency.
See, King had tuberculous, and his appointment to VP was more of a lifetime achievement award. King was so sick, he didn't even attend the inauguration in Washington D.C. — he was in Cuba and was actually sworn in there, making him the only VP to be sworn in outside of the States. King died a little over a month after the inauguration, meaning President King likely would've gone down as yet another William Henry Harrison. Now, under those rules of the time, the President Pro Tempore became President. If that happened, David Rice Atchison is President. Again.
Why again? Well, if you know Atchison's name it's through a little foible where he was actually President for a day … from a certain point of view. Zachary Taylor's 1849 inauguration fell on a Sunday, and Old Rough and Ready refused to work on the Lord's Day. So, technically, Atchison was President that Sunday, because he was President Pro Tempore then as well. That is really a lot of bunk (the old President is still President until the new guy gets sworn in) so he wasn't really President, but in 1853, in the above disastrous scenario, he most certainly would have been.
Funny thing is, he wasn't a whole lot different than Pierce — they were both pro-slavery Democrats, and Atchison was so gung-ho about this, he actually resigned his Senate seat to lead pro-slavery forces into Kansas to intimidate anti-slavery settlers. Pierce was a pretty bad President, but if that train had been just a little bit meaner, we would've ended up with someone far, far worse.