White holes were really cooked up as a way to explain Quasars. At the time when some research was being done, the age of the universe (relating therefore to distance) was calculated to be less than it is now. The apparent "brightness" of the objects seemed impossible for any known body, and it was postulated (although never widely accepted) that these could White Holes, where the matter that was seemingly lost in a Black Hole was blasted back into the universe.
I would hasten to correct one statement however; the notion that a black hole "absorbs mass and makes it disappear from this universe" is very much a topic of current debate. This is a central issue in theoretical physics called "The Information Paradox", popularly. For any Unitary system, which quantum physics currently is telling us we're in, information is never LOST. This has led to various ideas being floated, from the absurd to the likely.
The leading candidates are that, yes, Black Holes are unique regions of spacetime and in that place matter is crushed out of existence, to be emitted as Hawking Radiation which would violate Unitarity. The other is that the information is "encoded" so to speak, in minute fluctuations of the event horizon of the black hole. Others have posited (as they do since Einstein's equations predicted Black Holes) that Black Holes don't exist. Instead there are arguments for the notion that a black hole is always JUST prevented from forming as the star collapses. This generally involves models of inhomogeneous gasses and their collapse, vs. expected vacuum pressure, etc, and are not widely accepted or even fully formulated.
Finally, as always, there are those who believe that in defiance of many laws that would say otherwise, the information lost inside a black hole is only lost until it evaporates... leaving a super dense remnant. This... is frankly silly from my point of view based on my limited understanding of how much information can be encoded in a given region, but it seems unlikely. Thorne or Hawking... pick a side lol. Oh, as for how a black hole LOSES its mass, that is currently believed to be through a process called Hawking Radiation, but that is entirely theoretical as well and depends on a particular understanding of how particle anti-particle pairs/particles moving through time in the region of the black hole. Right now to be blunt, they are thought to evaporate in a thermodynamic process in accordance with GR, but not The Standard Model
