... when the fluid bathing the core heats up and starts to form voids -- aka bubbles.
In a reactor design producing a negative void coefficient, the voids will cause the chain reaction to slow down. This does help the reactor self-protect against overheating and meltdown.
In a reactor design producing a positive void coefficient, the voids will cause the chain reaction to speed up. The result is a reactor that can get away from you very fast, and that is completely reliant on external safety systems.
The Chernobyl reactors had a positive void coefficient as one of their serious design flaws, and this played a role in producing the conditions that created the meltdown.
However, NO reactor design in current commercial use is meltdown-proof. Three Mile Island's reactors were designed for a negative void coefficient -- and look what happened there.
So under certain accidental conditions they produce the material for A-bombs? So this is a dual use technology which can slip up and make nukes? I hope to God somebody is on top of this, but I'm confident that they are. Nevertheless, this points out some of the serious risks in nuclear energy. I think a future without it is the way to go.
You're thinking of a breeder reactor, perhaps? That's different. Breeder reactors can be designed with a negative void coefficient, but I still wouldn't trust one. They're kind of notorious, safety-wise.