Some supernovae and gamma-ray bursts are thought to accompany a black hole formation. In the process of a black hole formation, a central core becomes hot and dense enough for hyperons and quarks to appear. In this study, we perform neutrino-radiation hydrodynamical simulations of a stellar core collapse and black hole formation taking into account such exotic components. In our computation, general relativity is fully considered under spherical symmetry. As a result, we find that the additional degrees of freedom soften the equation of state of matter and promote the black hole formation. Furthermore, their effects are detectable as a neutrino signal. We believe that the properties of hot and dense matter at extreme conditions are essential for the studies on the astrophysical black hole formation. This study will be hopefully a first step toward a physics of the central engine of gamma-ray bursts.