At Three Mile Island, and subsequently, Chernobyl (Ukrainian, Chornobyl) there were failures of the reactor coolant system. Both were water-cooled, TMI was water-moderated, and Chornobyl was graphite-moderated.
Ideally, in a water-moderated thermal reactor, the loss of water cuts off the supply of sufficiently slow neutrons to maintain the chain reaction. But if the water pumps fail or are shut off, this doesn't happen. In a graphite-moderated reactor, the graphite goes on supplying slow neutrons.
But the water ceases to keep the fuel rods cool, and they eventually melt or weaken enough to lose the proper structure. The reaction does not turn into a bomb, but the hot radioactive fuel rods can melt through the floor.
They really cannot melt all the way to China through the Earth!
The Earth itself is kept molten by its own radioactivity.
The Integral Fast Reactor, cooled by liquid sodium (sodium melts at just about the boiling point of water), is immune to the problem of steel high pressure water pipes rusting and losing pressure. Its coolant has a high boiling point, and is not under pressure, in fact it can perfectly well be supplemented by a bath of liquid sodium cooling itself by convection.
The design is also different from the Pressurized Water Reactors (PWR) in current use, in that its fuel rods are metallic, and conduct heat better than the ceramic oxide type PWR fuel rods.
But the key feature in surviving loss of power and loss of coolant pumping is, that the geometry of the reactor core design is sensitive to thermal expansion in a way that lowers the neutron flux to a sub-critical level if the temperature rises above normal operating range.
The power reactor chain reaction, unlike the cataclysmic chain designed for a bomb, is a delicate balance. Ordinarily, there are just enough neutrons coming from the atomic fissions and being captured by fissile nuclei to maintain a steady rate. There are control rods, which absorb neutrons, to diminish this rate if less power is required, or to shut down entirely. As fission products which also capture neutrons build up in the fuel rods, the control rods are pulled slightly further out.
But when the IFR core gets too hot, its geometry changes. The spaces between the fuel rods enlarge, and neutrons escape instead of maintaining the reaction.
No, they don't escape and terrorise the landscape, they're captured by the shielding. The reaction shuts down.
The loss of coolant scenario was actually tested in the first week of the very month (April 1986) that the Chornobyl accident happened. In the first instance, power to the prototype reactor's coolant pumps was shut off. The reactor simply shut itself down. So for another test, the entire electrical system that would be taking away the heat was isolated from the plant. Again it just quietly shut down. As designed. Of course, the coolant fluid itself, the sodium, was not lost. It remained quietly in its unpressurised pipes.