The problem here is purity; there is simply not enough fissionable Uranium or Plutonium in a small enough are for the neutrons released by each split to split, on average, more than one other atom.
Alrighty, so fission basically only occurs in two elements, and more specifically, one isotope of each. I'll use Uranium as an example. Most uranium is U=238; that is, it has 238 particles in its nucleus. The stuff that actually splits is U-235, and it only splits when it gets hit by a neutron. This produces two random atoms of different elements, usually ridiculously unstable (and the source of most of the radiation) and a bunch of neutrons, which can then split more atoms. In a supercritical (i.e. a nuclear weapon) chain reaction these neutrons will spark off more than one new split per atom split, exponentially increasing the energy released until blah blah horror horror death death. In a critical reaction (i.e. normal reactor function), the spray of neutrons from each split on average splits only one more atom, meaning the release of energy goes at a steady, useful rate. In a subcritical reaction (i.e. this kind of reactor out of coolant), less than one new split is caused by each split, meaning the whole shebang just kind of burns itself out. The main way to control how many atoms each split sets off is the density of U-235 atoms; if they're all close together, there's a bloody good chance that many of the neutrons will hit a fertile atom and blow it up; if they're far away from one another, and especially if there are things that are blocking in the way (i.e. literally anything but fissionable material, but especially non-fissionable uranium (like 95% of the fuel pellets), graphite, boron(?), and water, most of them are going to just fizzle out and bounce around a bit before losing too much speed to actually set off a split.
Hopefully that was lucid and correct despite me being up five and a half hours later, or three and a half hours earlier, than usual.
Well that is correct ; now let's add one thing. The water is used both to cool the bar to fuel, to extract the heath for energy production and to slow the neutrons to an energy were they are more likely to interact with U235 core. In the absence of water, the neutron have too much energy and won't interact often enough to maintain chain reaction, but that's assuming that the fuel retain it's shape.
Indeed, if you get more fuel close together you'll make interaction more likely again and chain reaction could resume.
The question is : could the bars of fuel melting get enough liquefied fuel at the bottom of the reactor to get chain reaction running again? And don't ask me I've no idea.