This question might sound quite odd and is a mix of philosophy and physics. Suppose we observe a star that is 50 million lightyears away, and suppose it is a type of star that has a lifespan of only 30 million years. The question is, does this star "exist" in our reference frame?
The reasoning for why you would say "no" is simple: the star's lifespan is shorter than the time it took for light to travel to us. People who believe this would say that the star doesn't exist anymore and what we are seeing is only the photons from the star.
But the reasoning for why you might say "yes" is a bit more abstract. According to general relativity, all information must travel below the speed of light. This means that we don't just see the star, we also feel it's faint gravitational force, we also receive it's heat, and any other ways the star could affect us. By all measurable accounts, the star is still there. There is no measurement we can do that shows it's absence, so how can you argue it isn't real?
Think about it this way: if I were to try and prove the screen infront of me is real, I would do so by making measurements. I could say I see it, and I can feel it(electromagnetic effects from the atomic bonds). This is the exact same argument as with the distant star, I can see it and "feel" the gravitational effects. The star is real in the same way everything nearby to me is real.
One last extension of this idea for those who lie in the "yes" camp: suppose we live in a universe with positive curvature. This would mean that if you departed from earth in a straight line and mainted this without acceleration you would eventually reach earth again(okay not exactly but you know what I mean). Now imagine that both you and the earth are immortal. Eventually the observable universe would grow large enough that you would be able to "see" the earth in the distance, and would see a much younger version of yourself. Now if that distant version of you is "real" does that mean there are now two yous?