Well, last century one of the most shocking revelations by Einstein (with foundational work from other scientists too) was that the universe is one big jumbled mess of different time-flows!

On a tangent note: how exactly the "fabric" (the "space-time-continuum") does not rip itself apart due to different flowing speeds of time at different locations, is beyond me!?

Like seriously, right over there, at that spot to your left time is flowing at Rate-A, and just over there at another spot to your right, time is flowing at Rate-B. So again you'd think that would tear the Universe to shreds due to mismatched time flow!? Seems like that sort of thing would just rip a universe apart!

And as it turns out, with a heavy object for example, the space-time-continuum does get distorted and kinda ripped and twirled around (in a process called "frame dragging").

So ya: this sort of stuff actually does mess with the space-time-continuum! We've detected the ripples of space-time being messed with and distorted in this fashion, using the LIGO gravity wave detector, as distortion waves flow past our planet.

Anyways back to the time.

So right now, your current time, and my current time match (in terms of how fast a second ticks). Pretty close at least.

That means if a 3rd party observer was just sitting and looking at us communicate with each other, typing on our keyboards, he'd see that your time-flow is the SAME time-flow as me, here together on planet Earth.

But, you might have heard of that famous (and now "cliche!" but true) thought experiment:

If you climb onboard a spaceship and travel really really fast to the nearest star system, then come back, for you only a couple of years of subjective time might have passed.

Meanwhile here on Earth 500 years would have passed!

So in that case our clocks got disaligned (in terms of how fast a second ticks for you, or for me, as observed by that 3rd party sitting there and watching our lives unfold).

So what this means is, that the answer to your question is yes and no!

It all depends upon your frame of reference.

To you, at this current rate of time-flow, from your current frame of reference: YES! Black holes TOTALLY exist. They are real. They are not gone. Not dead. No large black hole has died.

But from the frame of reference of the person falling into a black hole, as they then look up and say outloud: "Wow I just saw the Universe end and die! And now this black hole is evaporating..."

That just simply means their time-flow was so-so-so-so-incredibly-painfully slow compared to yours, that for them to just form the first word of the sentence "wow" would have taken EONS of time, from your perspective, watching them fall in.

TL/DR:

Yes, the person falling into the black hole (from their reference frame) will think, "Wow! I just now fell in and the Universe ended! That's so weird!?"

But it will take vast eons of time for them, for their brain cells to even fire, and for them to have that thought, and for them to move their lips and say that thought.