Flexible electrodes that allow electrical conductance to be maintained during mechanical deformation are required for the development of wearable electronics. However, flexible electrodes based on metal thin-films on elastomeric substrates can suffer from complete and unexpected electrical disconnection after the onset of mechanical fracture across the metal. Here we show that the strain-resilient electrical performance of thin-film metal electrodes under multimodal deformation can be enhanced by using a two-dimensional (2D) interlayer. Insertion of atomically-thin interlayers - graphene, molybdenum disulfide, or hexagonal boron nitride - induce continuous in-plane crack deflection in thin-film metal electrodes. This leads to unique electrical characteristics (termed electrical ductility) in which electrical resistance gradually increases with strain, creating extended regions of stable resistance. Our 2D-interlayer electrodes can maintain a low electrical resistance beyond a strain in which conventional metal electrodes would completely disconnect. We use the approach to create a flexible electroluminescent light emitting device with an augmented strain-resilient electrical functionality and an early-damage diagnosis capability.