If a Leaf Falls in the Forest...
When stars or big gas clouds fall into a black hole, it makes a heck of a racket. Magnetohydrodynamic effects in the accretion disc heat the infalling matter to millions of degrees, resulting broad spectrum emission of electromagnetic radiation, and powerful jets of charged particles can be sources of great amounts of synchrotron radiation, much of at longer wavelengths.
How about dark matter? Is there any reason to believe that it doesn't just fade softly and silently away as it fall into the black hole, carrying nothing but mass and a bit of angular momentum? It, presumably, cares nothing for electromagnetic fields or hydrodynamic pressure.
Your amateur cosmologist speculates, however, that not a whole lot of DM meets that fate. My reasoning is based on the fact that the dissipative mechanisms (friction and radiation) that allow baryonic matter to condense far more strongly than dark matter are not available to it. Any thoughts? I haven't seen anything on this yet.
UPDATE: Here is a professional's take: