Over a broad range of initial inclinations and eccentricities an appreciable fraction of hierarchical triple star systems with similar masses are essentially unaffected by the Kozai-Lidov mechanism (KM) until the primary in the central binary evolves into a compact object. Once it does, it may be much less massive than the other components in the ternary, enabling the eccentric Kozai mechanism (EKM): the mutual inclination between the inner and outer binary can flip signs driving the inner binary to very high eccentricity, leading to a close binary or collision. We demonstrate this Mass-loss Induced Eccentric Kozai (MIEK) mechanism by considering an example system and defining an ad-hoc minimal separation between the inner two members at which tidal affects become important. For fixed initial masses and semi-major axes, but uniform distributions of eccentricity and cosine of the mutual inclination, ~10% of systems interact tidally or collide while the primary is on the MS due to the KM or EKM. Those affected by the EKM are not captured by earlier quadrupole-order secular calculations. We show that fully ~30% of systems interact tidally or collide for the first time as the primary swells to AU scales, mostly as a result of the KM. Finally, ~2% of systems interact tidally or collide for the first time after the primary sheds most of its mass and becomes a WD, mostly as a result of the MIEK mechanism. These findings motivate a more detailed study of mass-loss in triple systems and the formation of close NS/WD-MS and NS/WD-NS/WD binaries without an initial common envelope phase.