I don't think "absorb" is the word I would use to describe this effect. Space-time itself is simply bent, not destroyed. When he says that the black hole is dragging spacetime, he doesn't mean that it's being destroyed or absorbed. It's more like a whirlpool, where the water is dragged in to become part of the spinning vortex. In fact, relativity can predict the curvature of spacetime inside of a black hole, though such predictions could never be proven. The only sense in which spacetime is absorbed is that we can no longer communicate with it. Theoretically, though, it should still exist.