What occurs is that the innate immune system, macrophages specifically, recognises the ink as an invader and they engulf the ink, tiny drop by tiny drop, then just hang about, their job done, until they die. When they die (apoptosis) they themselves are tidied up by the immune system and the cycle continues with generation after generation of macrophage holding the ink in place, but every time that happens a little ink is lost causing the edges of the tattoo to become fuzzy and fade over time.
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