The electron capture is an interesting kind of nuclear transformation. Rather more frequently you can find the opposite - a fully stripped atom decays by $\epsilon$-decay no more.
To enhance the decay, you - potentially - could modify an electron shells to increase the capture probability. Here is one claim with ultrastrong magnetic field e.g. http://cpl.iphy.ac.cn/fileup/PDF/2012-4-049701.pdf. Something like this has a potential for a processing of a nuclear waste, but the fields are crazy.
Another environment, where you can find heavily modified electron "orbits" is in heavy stars. There is high electron density with high electron energies and the electron can be captured by a nucleus from a continuum. And even (under normal conditions) stable nuclei can capture these high energy electrons
At even higher temperatures (>1GK), there can be a lot of $e^+ e^-$ pairs produced and even a positron can get captured by a nucleus.