Despite what people may have heard, nuclear reactors are inherently safe. In the event of a need to secure them an operator needs to simply shut it down by lowering the control rods. Normally this is controlled over a number of hours but it can be very rapid if needed (less than 1 second), and this is referred to as a scram.
A scram is a sudden reactor shutdown. When a reactor is scrammed, automatically due to seismic activity, or due to some malfunction, or manually for whatever reason, the fission reaction generating the main heat stops. However, considerable heat continues to be generated by the radioactive decay of the fission products in the fuel. Initially, for a few minutes, this is great - about 7% of the pre-scram level. But it drops to about 1% of the normal heat output after two hours, to 0.5% after one day, and 0.2% after a week. Even then it must still be cooled, but simply being immersed in a lot of water does most of the job after some time. When the water temperature is below 100°C at atmospheric pressure the reactor is said to be in "cold shutdown". They can operate at these conditions nearly indefinitely.
As for chemical spills, they are almost always caused by human error, and as the humans are no longer operating them, it is less likely for this event to occur.