I think the problem in understanding this is the idea of "space being sucked into a black hole." The reality is matter is "sucked" into a black hole. Space is warped around the black whole, but space is not "sucked" into anything.
Here's the issue. What is space? You can't touch space (or better, the space-time continuum). So, one view is that space is where matter exists. Yet, you could have "space" without matter in it (empty space). Or you could have space with matter in it (like, say, the planet earth. Note that matter can only exist in space. So it is not possible (at least in this universe) to have matter without space.
In that case, what does "warping" of space mean? One thing we can do is take a beam of light and have it traverse an area of space. If the space is empty, the beam of light will follow a straight line. But if there is some matter in that space and the beam goes near the matter, its path will curve a little bit (if, say, the matter was the earth). The matter has warped space. The matter is not sucking up space, but the matter interacts with space in such a way that the path of a light beam is no longer a straight line.
As the matter occupying a section of space increases (its density increases), the warping of space gets more severe. The beam of light bends more and more. Also, the closer the beam gets to the matter, the more it bends. Interestingly enough, the bending is parabolic, just like a comet flying past the sun. If the mass gets large enough, and the beam of light gets close enough (the even horizon), the path of the light bends so much that the light orbits the object. This object is known as a black hole.
Note that if the light beam is outside the event horizon, then the path is bent, but the light does not get "sucked into" the black hole.
We now get to your question. The volume of space does not change, just how other pieces of matter and how light beams interact with that space changes (space is warped). Now, "weirdness" near a black hole does occur. As light heads towards the warped space, it shifts color towards the blue end of the spectrum (similar to Doppler effect). Once the light goes past the black hole, its color shifts toward the red end. Time also changes near a black hole (it slows down considerably).
So, how do you measure space? One way is to send a pulse of light towards a mirror and measure the time it takes the light to go to the mirror and back. This round-trip time then gives the distance as D = T * C / 2, where D is the distance between you and the mirror, T is the time you measure for the pulse to go to the mirror and back, and C is the speed of light. We divide by 2, because the time is the time down and back.
So, lets say we are far away from a black hole, but we want to measure the "space" near the hole. We send a space ship near the black hole, but outside of the event horizon. The ship has a mirror on it and we send a pulse of light to the mirror to measure the distance. As the light pulse comes out of the gravity well of the black hole, the pulse gets elongated by the curved space. In addition, the path the light travels is curved due to the warping of space.
The result is we measure a long time, meaning that D is very large. As the ship gets nearer to the event horizon, that time heads towards infinity and D also heads towards infinity (if the ship crosses the event horizon, we will never see the reflected light and the time and distance could be considered infinite. So, it would appear that space has gotten infinitely huge near the black hole. The reality is, space has just been seriously warped, and are measuring technique is no longer valid for measuring space, since we are really measuring the warping of space, not space itself.