Ionization of matter by energetic radiation generally causes complex secondary reactions that are hard to decipher. Using large helium nanodroplets irradiated by extreme ultraviolet (XUV) photons, we show that the full chain of processes ensuing primary photoionization can be tracked in detail by means of high-resolution electron spectroscopy. We find that elastic and inelastic scattering of photoelectrons efficiently induces interatomic Coulombic decay (ICD) in the droplets. This type of indirect ICD even becomes the dominant process of electron emission in nearly the entire XUV range in large droplets with radius ≳40 nm. Indirect ICD processes induced by electron scattering likely play an important role in other condensed-phase systems exposed to ionizing radiation as well, including biological matter.