Do you mean fuel rods in nuclear reactors at the time of the decimation of the population?
In that case, nothing. At least not in any reasonably designed reactor.
Most reactors have automatic failsafe mechanisms to cut off and stop the reaction if there are no people to attend to the reactor.
They are designed in a way that the process of the reaction is not self sustaining and in need of constant upkeep. In the event of trouble (like no people to attedn the reactor, or the reactor failing due to some technical error), the reactor will stop this "upkeep" of the nuclear fission, which in itself is enough for the reaction to stop, but the reactor will also automatically enact further safety measures.
The fuel itself won't get hot enough without the nuclear fission going on, so it will not catch on fire or melt.
It will just sit there decaying, as it would have if it wouls be still in the ground.
to expand on what i wrote about a non self sustaining reactor:
modern, reasonably designed reactors basically don't need to do anything to stop the nuclear reaction, they are built in a way that fission cannot take place on it's own. What does need constant work is the enabling of the reaction. So if a reactor fails, it's not the containment of the process that stops, but the enabling of the process.