How do we know distant stars still exist The Pleiades are 450 light years away. Thus when we see the twinkle in the night sky the light that hits our retina emanates from the year 1569 or so. On that proviso; how can we be sure that the star is still alive given the fact that we are seeing light from hundreds of years ago.
We don't know from sensory evidence.  As far as we can tell, no information ever moves faster than the speed of light, so we are always at least 450 years out of date for anything happening in the Pleiades.

The only evidence we have is inferential: As far as we can tell (and we've looked real hard at this) the world works the same both here and at the Pleiades.  And as far as we can tell (and, once again, we've looked real hard at this) stars like those in the Pleiades don't just disappear or go out in only 450 years -- it takes millions of years.

So, based on what we observe of them as of 450 years ago, and based on what we know of how stars work, we conclude that they are pretty much the same "today" -- though, really, what we're concluding is that when we observe them 450 years from now, they'll still look pretty much like they do today.

This is all inferential, but I'd bet just about anything on it.  (If only I were here in 450 years to collect!)