Huh, What of Dark Matter and Frozen Stars?

Okay we know that whatever Dark Matter is it exists. And obviously it has mass and gravitational attraction, because that's how we discovered it. So what of Frozen Stars aka Black Holes? Wouldn't they vacuum up Dark Matter and prevent it from escaping just like any normal baryonic matter?

Now since Dark Matter, whatever it is, is thought not to interact with other particles or itself other than gravitationally it would not fall in very readily. This is because in a universe of pure gravity without interaction everything would go into big orbits without losing energy (at least in my thought experiment, I could be wrong). So the Frozen Star would have to intersect with the path of the Dark Matter.

Further thought. If a Neutron Star is massive enough to overcome the 'pressure' of the neutrons to collapse them into just quarks would the density of the quarks in the center gradually capture enough Dark Matter to cause the formation of a Schwarzchild radius and the ultimate collapse into a Frozen Star? This would probably only occur over very long time periods. Billions of years. Since Dark Matter interacts so weakly.