From the introduction to a paper describing a recent series of experiments on the topic (experiments which no evidence of decay rate change, to four significant figures):
Extensive research has shown that the decay rate of a radioactive nucleus is independent of its environment, except in those instances involving electron capture, internal conversion, or high external magnetic fields [Hahn et al., 1975].
The energies involved in nuclear transitions are very much larger than the energies involved in chemical or electronic transitions in atoms and molecules --- so much so that, no matter what the chemical environment is like, it's safe for chemists to treat nuclei as more or less inert. A process that could change a nuclear decay rate would be so energetic that its side effects would completely ionize the atoms and their neighbors.
Here's an example of a nuclear process that changes a decay rate, but not in the way you had in mind. One reason that nuclear waste is more dangerous to deal with than nuclear fuel is that the waste products have a shorter half-life than the fuel products, by a lot.
There we're turning long-lived uranium into stable and short-lived fission fragments and medium-lived plutonium.
The decay rate changes because the nucleus is transmuted into a different nucleus, but the decay rate of each nuclide is well-defined.
Note that the contribution of nuclear fallout to background radiation is quite small.
