Yes. In fact, when a black hole is formed it normally occurs in a huge explosion of a sufficiently massive star. Most of the material of the original star is ejected to outer space, maybe to form new stars and systems. On the other hand, the core of the star will be too heavy to support its own weight and will collapse without stop. That will be the black hole.
Now, if our ideas are correct, a black hole does not last forever. If we add quantum theory to the picture, then it will lose some of its mass constantly. That means it will become smaller and smaller as time passes by (assuming it doesn’t swallow anything during that time). Eventually the black hole will disappear in a not very spectacular manner.
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