The runaway reactor at Chernobyl went subcritical by prompt dispersal.

Yes, the nuclear reactor can be useful when it comes to making nuclear weapons. Uranium can be lowered into the operating reactor and can be bathed in the neutron flux to become (through nuclear transformation) plutonium. Plutonium is ready to be shaped into the subcritical masses used in nuclear weapons.

If the control rods in a nuclear reactor were somehow to be instantly "jerked" out of the reactor, the reactor would go supercritical. If they were pulled at a normal rate and all of the control rods were pulled out, the reactor would start up and heat up and would end up running far too hot. Any one of several safety systems would shut the reactor down before this could happen. If the safety systems were disabled, the reactor would overheat and a meltdown may occur.

A subcritical reactor works by using neutrons from a source outside the reactor, instead of from within. This means that it can operate without being critical or nearly critical.

The neutrons are provided by bombarding a spallation target, which could be lead, mercury, bismuth, or some other heavy element, with high energy protons that have been accelerated in a particle accelerator. When such a proton hits a lead atom, it can cause a cascade of high energy neutrons. These are passed into, or even generated within, the reactor itself.

In the reactor, the reaction is somewhat different from what goes on in a conventional nuclear reactor. Both have neutron capture and fission going on. But the subcritical reactor does not require a critical mass, and so the radioactive materials in it can all be exposed to neutrons continually without any need to remove them for refuelling as the lead medium and lead produced can be distilled out gradually while new fuel is added. The result is that the waste is almost entirely made up of radiologically inert materials.

Thorough computer modelling has been done, and reveals that the electrical power needed to drive a reactor of 650 mW electrical output is about 65 mW. The fuel can be thorium, uranium, or nuclear waste, and there is enough thorium to provide power for millennia, if things work as projected. Also, the reactor itself cannot melt down, and cannot be used to make bombs. But it may give us the ability to consume, and render inert, our nuclear waste.

No plant of this type has yet been built. There are a number of plants in planning, and a realistic hope that they will work.