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.