It's unclear what it is you wish to talk about regarding black holes. They can not only form and die, but they can do other things like combind with other masses including other close black holes. They can also produce very bright accretion disks, if they are in the process of absorbing a neighbor. That's how we found the first BH, IIRC.
Well, I guess you are being confused by
@vincenzosassone 's sentence. They are saying that:
Black Holes have two foundamental points of their lives: the birth and the death, as all the stuffs in the universe. [sic]
I guess vincen (I am shortening it, okay?) is meaning to say by the word "fundamental" (I don't agree with it though) that blackholes too have the same stages of life like we human beings have: birth and death. And they are also further stating that they don't want to talk about the death of it but the birth of it, though in pretty vague terms. I am not blaming you, Helio, for not understanding; but, I have to state that vincen is pretty vague and anyone could be confused.
Now, I am gonna talk to vincen. Well, vincen, blackholes are classified into three types: stellar-mass blackholes, supermassive blackholes and (this one is pretty theoretical, but possible) primordial blackholes. Stellar-mass blackholes were formed when gigantic stars undergo supernova and their cores collapse to infinitesimally (sorry, Cat, I couldn't find any other word to use) small objects with infinite density. Now, according to theory, primordial blackholes were formed during the first stages of the universe, id est, the big bang. Theory says that points of high density in the early universe might have collapsed to form these blackholes. Scientists haven't found them yet, but they might soon. Now, supermassive blackholes. Scientists haven't yet found a perfect answer for the formation of supermassive blackholes. Some say that huge star clusters might have collapsed to form the blackholes. Some say that it's not possible as there were not too many stars in the early universe, as we have found many supermassive blackholes more than 10 billion light-years ago. It's up for debate.
Now, you were trying to avoid the death of blackholes. No proof of a dying blackhole has ever been found. But some state that blackholes will "evaporate" into nowhere in the extremely distant universe (I am not with the theory though.) As, blackholes are already points of nowhere, it's implausible to assume that they will evaporate into nowhere. Well, it's up for debate whether Hawking Radiation really makes blackholes evaporate, it's the only assumption for the "death" of a blackhole.