With the detection of gravitational waves from merging compact objects, a new observational window onto the fates of massive stars has been opened. To explain the observed mergers of compact objects, we need accurate knowledge about the evolution of massive binary stars. Yet, current population synthesis calculations often yield puzzling results, as they predict certain types of stellar systems in large numbers, which are rarely observed. Whether this is due to observational challenges or due to errors in the underlying evolutionary models, is one of the major open questions in massive star research. In this proposal, we tackle two crucial stages of massive binary evolution that are predicted in large numbers, but so far rarely observed: Systems containing an OB-star accompanied by an X-ray-quiet black hole (BH) and systems where a hot, envelope-stripped star is outshined by its OB-type companion. In both cases, the (compact) companion hardly leaves any trace in the optical beyond a suspicious, small He II disk-like emission. To identify the nature of the companion and distinguish between a BH and a stripped-star companion, UV spectroscopy is the only viable tool. With the unique capabilities of the HST, we will perform a pilot study for two prototypical systems in the Galaxy and the LMC that harbor either a BH or a stripped star companion. By determining the presence of tracing ions and the wind parameters of the stars, our study will confirm or deny the existence of the presently only known dormant BH in the Milky Way, marking an anchor point for our understanding of massive binary evolution and defining a framework for future observations of stripped stars.