Relaxation processes following inner-valence ionization of a system can be modified dramatically by embedding this system in a suitable environment. Surprisingly, such an environment can be even composed of helium atoms, the most inert species available. As demonstrated by the examples of Ne and Ca atoms embedded in He droplets, a fast relaxation process [Interatomic Coulombic Decay (ICD)] takes place merely due to the presence of the He surroundings. We have computed ICD widths for both 4He_N and 3He_N droplets doped with Ne and Ca and discuss the findings in some detail. In the case of Ne, ICD is by far the dominating relaxation pathway. In Ca, atomic Auger decay is also possible but ICD becomes a competitive relaxation pathway in the droplets. ; Comment: 10 pages, 3 figures