It's more accurate to say life can occur.
Yes, when the sun has used all its nuclear fuel, life in the solar system will be impossible. When the universe has reached maximum entropy (heat death), then life anywhere in the universe will be impossible.
Now, if somewhere an environment stabilizes and remains stable, then evolution will stop whether the sun still shines or not. You see, evolution has some requirements above and beyond the existence of living organisms.
Sure, if you want to nit pick it. I could also point to the original analogy and say that the lightbulb could produce light assuming that the metal element is still connected across the anode and cathode, and that the battery terminals are not oxidized. I was simplifying a bit, but the meat of the explanation is still accurate.
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