The cusps surrounding the massive black holes in galactic nuclei are populated by stellar mass objects (as evidenced by observations of stars in the center of the Milky Way). These stars in orbit around the central black hole will interact and scatter each other. Occasionally a star will be deflected to pass near the horizon of the central massive black hole.
A main sequence star passing near a massive black hole will be tidally disrupted. Compact stars (white dwarfs, neutron stars or black holes) will remain intact and, if their angular momentum is large enough, will scatter out of the 'loss cone' of the massive black hole. On successive orbits the compact stars will lose energy and angular momentum to gravitational radiation and eventually be 'swallowed up' by the massive black hole.