Is it possible for a giant black hole to crush under it's own gravity?

Is it possible for a giant black hole to crush under it's own gravity? ...the theory of the "bigbang" induce the possibility of a "bigcrunch" and this last phenomena supposes that all matter in the known universe would be reduce to a "singularity" crushing also all the existing blackholes!!!

There are supermassive black holes in the centers of many galaxies, including our own. Stars, gas and dust orbit the hole, eventually getting swallowed up by it. It is very likely that some stars will form "normal" black holes, and then get swallowed up. So that's another way for a black hole to absorb another.

In both these cases, the most likely outcome is simply one black hole with the mass of both initial holes combined. It's the same thing, more or less, when you drink a glass of water. Now the water is in you, and you mass a little more!

To answer your first question, can a black hole crush itself, well, that's what a black hole really is! It's a star that has collapsed so far that to escape from it you have to go faster than light. Since nothing can go that fast not even light can escape, so the star becomes black. Once you're in, you cannot get out, and so it's like an infinitely deep hole.

So sometime in the distant future, if things work out just right, the expansion of the Universe may slow, stop, then reverse. If true, then all the matter and energy in it will come back together into one gigantic big crunch, forming the biggest black hole possible.

For lots more info about black holes, I highly recommend Ned Wright's Cosmology FAQ, which has lots of answers to commonly asked questions about black holes and the Universe.