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The photons are originally created as gamma rays in fusion reactions. These photons are repeatedly absorbed and re-emitted in random directions by atoms. Eventually they work their way out to a level in the sun where they can escape. The time averages out to millions of years.
When the sun runs out of fuel it will become a white dwarf. The universe has not existed long enough for the earliest white dwarfs to have cooled to black. They are still sitting there radiating their residual heat, and will be for billions if not trillions of years.
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