You end up with what is called a 'Bose-Einstein Condensate'. This is what happens to ordinary matter. For objects such as black holes, absolute zero is not relevant because there is no way that the physics inside the black hole can make itself known to we outsiders. There is nothing that you can assign the concept of energy to.
Temperature is just another name for the average random kinetic energy of a collection of matter.
If you lower this kinetic energy by essentially slowing the particles of a system down, the system often collapses into a denser state if it is the thermal pressure of the system that is supporting it. A star, supported by thermal pressure, will collapse to a white dwarf or a black hole if its 'temperature' were reduced. But exotic objects such as black holes are different. The surface area of the black hole, according to Stephen Hawking and others in the mid-1970's can be thought of as a measure of its entropy, however, unlike for other systems upon cooling, the entropy of a black hole can never be decreased because the mass inside a black hole can never be reduced. J ILA physicists have achieved a temperature far lower than has ever been produced before and created an entirely new state of matter predicted decades ago by Albert Einstein and Indian physicist Satyendra Nath Bose.