Is it possible that, given the vast distance between Earth and a star, that a star that I see now may not exists anymore?
Adding on top of that, say we developed a space-craft that travels at light speed, or sub-light speed and send it to a distance solar system which planets may have life. Could it it be possible that by the time the craft has reached there, the star and it solar system is gone too?
Well, stars don’t just wink out of existence. Even after a supernoval explosion, core of the star still remains as a black hole or neutron star. But it is entirely possible that this has happened, and the light from the explosion hasn’t reached us yet. Smaller stars don’t explode as spectacularly–they bloat up into red giants, engulfing their inner planets.
Stars also move. Many of the stars you see aren’t where they appear in the sky, but we can track their motion and extrapolate to find where they actually are now.
If you got in a spacecraft and headed off at near the speed of light toward a promising solar system, and the sun had actually turned into a red giant before you left, then at some point along the way you could see it happen, and know that the rest of your trip isn’t worthwile. If that’s any consolation. 
“supernova”? That isn’t a word. I meant “supernova.”
Absolutely. Proxima Centauri is 4.22 lightyears away. If it blows up today at 12:57 pm eastern standard time, we won’t know about it for 4 years and 80 days. This is one of the biggest problems with astrology. Star positions that are supposed to affect us profoundly are not really in the positions we see them in. (The stars of my sign (cancer) are Asellus Australis, Acubens and Asellus Borealis. They are so distant and so far apart from each other it isn’t funny.)
As to the 2nd part of your question, possibly. But if we are s-m-r-t enough to send rockets at light speed to Proxima Centauri, then we’re smart enough to be able to look at the light from Proxima Centauri and deduce that it’s not in its death throws and will still be around for a few billion more years.
If you’re going to correct an error in a second post, at least spell the typo correctly 
No, see, she meant to put the period between the quotes.
Actually, wouldn’t it be supernovoid? Like an ova is ovoid…
Haaaaaa. My brain is clearly totally fried. And I have two days to
write a talk to give at a Very Important interview for a job I Desperately Want. sobs in desperation.
None of the local stars (local being within ~ 25 light years) are Giant Blue Stars with enough mass to explode and shed heavy elements all over the place. Vega comes close - yet these stars are so short lived (a scale of millions of years) that it’s unlikely to have life. I mentioned Vega because it, Altair (another blue star) and Deneb are in the Summer Triangle.
Deneb is about 1000 light years away. It’s a Super-Blue Giant (Searchlight) that would outshine the Moon if it were as close as Vega.
Vega is way too low mass to blow up. You need about 6 times or thereabouts the mass of the Sun for a supernova, and Vega has about 3.
In theory, Sirius B could explode, if Sirius A were to expand enough and start dumping mass on it. Sirius B is a white dwarf, and they do explode if the circumstances are right. This isn’t likely for Sirius though. Good thing: it’s about 9 light years away.
Betelgeuse will blow up someday, as will Antares, Rigel, Deneb… the question is when. Maybe tonight, or maybe not for thousands of years. Don’t hold your breath!
Source: http://www.seds.org/messier/m/m001.html
Source: http://chandra.harvard.edu/photo/0052/
What the Chinese saw on that day in 1054 was an event that actually occurred 6,000 years earlier. The same concept applies to everything you see in space. After all, the warmth of the Sun is energy that left the Sun approximately eight minutes before. So if the Sun were to blink out, we wouldn’t know it for another eight minutes.