How can a supernova affect black hole in a binary system? Suppose in a binary stars system there is a dying star and a companion black hole as they orbit around each other. My question is what will possibly happen to the black hole if the partner goes supernova? I understand that the kinetic energy from the supernova cannot destroy the black hole.
The likely result would either be a black hole-black hole binary system; a neutron star-black hole binary system, or the black hole and the compact remnant from the second supernova explosion would go their separate ways at reasonably high speeds.

You cannot disrupt a black hole in this way. In fact all that will happen to the original black hole is that it will likely get a bit more massive from accreting some of the supernova ejecta.