They deliver their energy to the molecules they interact with, causing a slight change in shape that triggers the nerve response we eventually interpret as sight. As with anything that’s causing work to be done in the technical sense, there is waste heat. The photon ceases to exist when its energy is fully absorbed, although you could argue it lives on in some sense in whatever heat emissions come later.
To the second part, photons never “run out of energy” they instead just become harder and harder to detect… dimmer in a sense. They shift further to the red end of the spectrum, becoming longer and longer waves, but they never just magically go away.
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