The progenitors of hydrogen-poor core-collapse supernovae (SN types Ib, Ic and IIb) are believed to have shed their outer hydrogen envelopes prior to the SN explosion. The primary mechanisms driving this loss are believed to be either extremely strong stellar winds, characteristic of massive Wolf-Rayet stars, or interaction with a close binary companion star. The precise nature of the progenitors and the relative importance of these two mechanisms remains an open question however, highlighting the importance of obtaining pre-explosion observations of these systems. We consider a scenario where the progenitor of the hydrogen-poor supernova was a massive star in a high-mass X-ray binary (HMXB), in which the companion to the progenitor has already undergone a core-collapse supernova in the past to produce a compact remnant (neutron star or black hole). Accretion from the massive star to the compact remnant can produce extremely bright X-ray emission, but also serves as a potential stripping mechanism for the hydrogen envelope, potentially resulting in a hydrogen-poor core-collapse supernova when the massive star reaches the end of its lifespan. Here we present the results from our initial search for such progenitor systems, as well as describe our ongoing monitoring program to find potential candidate systems by searching for X-ray counterparts to newly discovered optical transients in pre-discovery X-ray observations.