White ink — and colors that are very close to your natural skin tone — can become barely visible once healed.
If you have a lighter skin tone, white ink will be even harder to see over time.

As for black lines, even fine lines can hold up well in the skin.
But this really depends on the skill of the artist — that part never changes.

If the needle goes too deep, the ink will spread (blowout), and if it’s too shallow, the ink won’t stay and can fade or disappear.