Recycled dwarf galaxies can form in the collisional debris of massive galaxies. Theoretical models predict that, contrary to classical galaxies, these recycled galaxies should be free of nonbaryonic dark matter. By analyzing the observed gas kinematics of such recycled galaxies with the help of a numerical model, we demonstrate that they do contain a massive dark component amounting to about twice the visible matter. Staying within the standard cosmological framework, this result most likely indicates the presence of large amounts of unseen, presumably cold, molecular gas. This additional mass should be present in the disks of their progenitor spiral galaxies, accounting for a substantial part of the so-called missing baryons.