Light traversing a hollow-core photonic band-gap fiber may experience multiple reflections and thereby a slow-down and enhanced optical path length. This offers a technologically interesting way of increasing the optical absorption of an otherwise weakly absorbing material which can infiltrate the fibre. However, in contrast to structures with a refractive index that varies along the propagation direction, like Bragg stacks, the translationally invariant structures studied here feature an intrinsic trade-off between light slow-down and filling fraction that limits the net absorption enhancement. We quantify the degree of absorption enhancement that can be achieved and its dependence on key material parameters. By treating the absorption and index on equal footing, we demonstrate the existence of an absorption-induced saturation of the group index that itself limits the maximum absorption enhancement that can be achieved.