They simply propagate out away from the point of annihilation at the speed of light. Whether they get absorbed depends on what they encounter along the way. It's similar to what happens to the photons that leave your flashlight.
If the photons have high enough energy, they can in turn produce new electron-positron pairs. This bubble-chamber picture shows a positron (orange) entering from the lower left and annihilating with an electron in the bubble-chamber fluid. One of the photons (purple-dot path) produces an electron-positron pair (green) at upper right. The other photon (invisible) leaves the field of view.