Negative temperature coefficients of reactivity matter to keep an operating reactor stable and prevent rapid overpower accidents a'la Chernobyl. All modern reactors exhibit this characteristic. However, the vast majority of risk in reactors today is that the fission energy doesn't all come out at the moment of fission. Some of it (roughly 7%) comes out after shutdown as exponentially-decaying radiation of the fission products. This decay heat (as it's called) is the primary safety hazard of today's reactors because there's enough of it to breach the reactor vessel if something goes wrong (a'la Fukushima). The Fukushima chain reaction shut down perfectly after the earthquake. The decay heat removal systems failed after the tsunami came along. The decay heat melted the fuel and cladding without cooling.
MSRs and other advanced reactors have passive decay heat removal by making use of different coolants (molten salt, liquid metal, etc.) and natural circulation air heat exchangers.
MSRs and other advanced reactors have passive decay heat removal by making use of different coolants (molten salt, liquid metal, etc.) and natural circulation air heat exchangers.