A tattoo is permanent precisely because of where the ink ends up. The needle pierces past the surface and lays pigment into the dermis.
Reasoning by skin biology:
$\text{Epidermis} \rightarrow \text{sheds every} \sim 4 \text{ weeks} \Rightarrow \text{cannot hold pigment}$
$\text{Dermis} \rightarrow \text{stable collagen + resident macrophages} \Rightarrow \text{traps pigment indefinitely}$
Once in the dermis, ink particles too large to be cleared are captured by macrophages and fixed within the fibrous matrix, so the design stays visible for life and may even resist early putrefaction - which is why forensic experts rely on tattoos for identifying decomposed or unknown bodies. Some pigment also drains to draining lymph nodes, occasionally pigmenting them.
Layers deeper than the dermis (subcutaneous fat, deep fascia) are below the needle’s reach, and the superficial epidermis is far too transient to retain ink.
\[\boxed{\text{Tattoo pigment resides in the dermis}}\]