The recently discovered C-19 stellar stream is a collection of kinematically associated metal-poor stars in the halo of the Milky Way lacking an obvious progenitor. The stream spans across an arc of ~15° in the sky, and orbit-fitting suggests an apocentric distance of ${\sim} 20\, \mathrm{kpc}$ and a pericentre of ${\sim} 10\, \mathrm{kpc}$. The narrow metallicity dispersion of stars with available spectra, together with light element abundance variations, suggests a globular cluster (GC) origin. The observed metallicity ([Fe/H] ≍ -3.4), however, is much lower than that of any known GC. In addition, the width and velocity dispersion of the stream are similar to those expected from disrupting dwarf galaxies, and substantially larger than the tidal debris of GCs able to disrupt on C-19's orbit. We propose here an unconventional model where the C-19 progenitor is a dark matter-dominated stellar system with GC-like abundance patterns. We use N-body simulations to show that the tidal disruption of a ~100 pc King-model stellar component embedded in a ~20 km s^-1 cuspy cold dark matter halo yields debris consistent with C-19's observed width and velocity dispersion. The stellar component of the progenitor is fully disrupted, and is spread over two distinct streams, one corresponding to C-19 and another possibly hiding behind the Galactic plane. If such companion stream were found, it would suggest that dark matter-dominated dwarfs may also develop GC-like enrichment patterns, a finding that would inform our theoretical understanding of the formation of multiple populations in GCs and dwarf galaxies alike.