Lyric discussion by Hokieguy95 

When I first heard this I kept thinking what on earth a "Paper Sun" could mean. A "Paper tiger" is something we think is powerful but has no strength and is a chimera. So what on earth is a false sun? Def Leppard has always disliked organized religion. Could several lines be a cryptic play on words with Sun meaning "Son" or "Savior"...The Son of God? Could it be a statement that Christianity is a joke and that people who rely on Christ are living on a "paper son" or "dream", putting their faith in something false. "I don't believe in you" (No belief in God or the Savior) you've come undone (people get carried away in religion) Blind to all the damage done (how organized religion hasn't been helpful.

I know this is a stretch, but I'm convinced some of the lines are a sly jab at religion.
Of course Cheesemaesto's take is probably the best straightforward meaning.

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