* Betelgeuse is about 642 light-years away. This means it takes light from Betelgeuse 642 years to reach Earth.
* We see things as they were in the past. When we look at Betelgeuse, we are seeing it as it was 642 years ago.
* If Betelgeuse died hundreds of years ago, we wouldn't know yet. Even if it exploded as a supernova hundreds of years ago, the light from that event wouldn't reach Earth until hundreds of years after its actual death.
Therefore, it is possible to see a star even if it has died hundreds of years ago because the light from that star continues to travel through space. We would only know about its death once the light from the event reached Earth.
The same applies to other stars and celestial objects. Everything we observe in the universe is a snapshot of the past, with the further away objects showing us even older versions of themselves.