I hope this doesn't end up becoming a "proof of concept" of the China Syndrome. Naturally it won't bore a hole through one side of the Earth and come out the other, but would be pulled to the center (burning all the way) into the core of the Earth.
"The China Syndrome" as portrayed in popular writing is a joke
Let's say, god forbid, the containment vessel melts through (remember, it IS designed to try and prevent that - again, see TMI), MOST of the slag pours out - critical here is that SOME - even say a few ounces is left behind. You now have less mass. Some of the mass will now evaporate, and condense on the walls of the containment building (from what I understand, it's actually designed that MOST/all will do so, but...), so now you have LESS melting into the earth - now, the earth itslef say starts to melt - what happens? Yep, more heat and more radioactive mass is pulled away, evaporates, coats inside of building, again, diluting and cooling the slag - fairly quicky, the slag gets below the temp it CAN melt earth, and it stops. HOW quickly is this is the question?
One real example - let's look at Chernobyl - folks, the core totally slagged, and there was NO containment vessel, or containment building. How far did the core go? Answer, it's in the basement of the building, and yes, it's been seen by humans (ooops - the guy realized once he turned the corner and ended up looking at it he was dead), but there was no 'China Syndrome'.
This is a picture of part of the core - there was a TV show that showed more