Context. The C-19 stellar stream is the most metal-poor stream known to date. While its wth and velocity dispersion indicate a dwarf galaxy origin, its metallicity spread and abundance patterns are more similar to those of globular clusters (GCs). If it is indeed of GC origin, its extremely low metallicity ([Fe/H]=‑3.4, estimated from giant stars) implies that these stellar systems can form out of gas that is as extremely poor in metals as this. Previously, only giant stream stars were observed spectroscopically, although the majority of stream stars are unevolved stars. Aims. We pushed the spectroscopic observations to the subgiant branch stars (G ≈ 20) in order to consolate the chemical and dynamical properties of C-19. Methods. We used the high-efficiency spectrograph X-shooter fed by the ESO 8.2m VLT telescope to observe 15 candate subgiant C-19 members. The spectra were used to measure radial velocities and to determine chemical abundances using the MyGIsFOS code. Results. We developed a likelihood model that takes metallicity and radial velocities into account. We conclude that 12 stars are likely members of C-19, while 3 stars (S05, S12, and S13) are likely contaminants. When these 3 stars are excluded, our model implies a mean metallicity <[Fe/H]> = ‑3.1 ± 0.1, the mean radial velocity is <vr> = ‑192 ± 3km s‑1, and the velocity dispersion is σvr = 5.9‑5.9+3.6 km s‑1. This all agrees within errors with previous studies. The A(Mg) of a sample of 15 C-19 members, including 6 giant stars, shows a standard deviation of 0.44 dex, and the mean uncertainty on Mg is 0.25 dex. Conclusions. Our preferred interpretation of the current data is that C-19 is a disrupted GC. We cannot completely rule out the possibility that the GC could have belonged to a dwarf galaxy that contained more metal-rich stars, however. This scenario would explain the radial velocity members at higher metallicity, as well as the wth and velocity dispersion of the stream. In either case, a GC formed out of gas as poor in metals as these stars seems necessary to explain the existence of C-19. The possibility that no GC was associated with C-19 cannot be ruled out either.