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The core can't "die" but I suppose you mean if the fusion reaction were to suddenly stop (and not be able to start again). Well, since the fusion is what keeps the sun supported, it would collapse on itself and create a mini super nova (I say "mini" because the sun is not big enough to do this on it's own).

This won't happen because of the suns small size. What will happen in several billion years, is that the helium will start to form carbon, oxygen, and other heavier elements. This change in the core reaction will cause the sun to turn red and expand. This outer layer will slowly expand out, leaving a small white dwarf (which will eventually turn into a red dward, then a black dwarf).

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14y ago

What else can I help you with?