They don’t age. I recently read some unused lore that talks about the earliest days of the city, when it was still a small settlement. There’s one entry that describes how Zavala fell in love with a non-guardian woman, that later died of old age. When he scatters her ashes he talks with Shaxx about love and they definitely make it seem like they don’t age at all. Very beautiful lore btw, I think someone posted a link to that on Reddit.
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We know for sure that every guardian, no matter their race, can’t die or weaken from age. It’s not really clear if changes to physical appearance can still happen though. I vaguely remember something about the Drifter and someone saying that he looked better in the past, but I wouldn’t take that as proof. It’s only a vague flicker in my mind and may also be a reference to scars or something similar, not old age.
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I think I remember The Drifter saying something like “vanish for a couple hundred years and everyone has gone soft” while talking about gambit. I might be wrong but if I remember that right then it speaks for itself.