We present multi-wavelength observations of SN 2014C during the first 500 days. These observations represent the first solid detection of a young extragalactic stripped-envelope SN out to high-energy X-rays ~40 keV. SN 2014C shows ordinary explosion parameters (Ek ~ 1.8 × 1051 erg and Mej ~ 1.7 M⊙). However, over an ~1 year timescale, SN 2014C evolved from an ordinary hydrogen-poor supernova into a strongly interacting, hydrogen-rich supernova, violating the traditional classification scheme of type-I versus type-II SNe. Signatures of the SN shock interaction with a dense medium are observed across the spectrum, from radio to hard X-rays, and revealed the presence of a massive shell of ~1 M⊙of hydrogen-rich material at ~6 × 1016 cm. The shell was ejected by the progenitor star in the decades to centuries before collapse. This result challenges current theories of massive star evolution, as it requires a physical mechanism responsible for the ejection of the deepest hydrogen layer of H-poor SN progenitors synchronized with the onset of stellar collapse. Theoretical investigations point at binary interactions and/or instabilities during the last nuclear burning stages as potential triggers of the highly time-dependent mass loss. We constrain these scenarios utilizing the sample of 183 SNe Ib/c with public radio observations. Our analysis identifies SN 2014C-like signatures in ~10% of SNe. This fraction is reasonably consistent with the expectation from the theory of recent envelope ejection due to binary evolution if the ejected material can survive in the close environment for 103-104 years. Alternatively, nuclear burning instabilities extending to core C-burning might play a critical role.