Carbon-deficient red giants (CDGs) are a peculiar class of stars that have eluded explanation for decades. We aim to better characterize CDGs by using asteroseismology (Kepler, TESS) combined with spectroscopy (APOGEE, LAMOST), and astrometry (Gaia). We discovered 15 new CDGs in the Kepler field, and confirm that CDGs are rare, as they are only 0.15% of our background sample. Remarkably, we find that our CDGs are almost exclusively in the red clump (RC) phase. Asteroseismic masses reveal that our CDGs are primarily low-mass stars ( M ≲ 2 M _⊙ ), in contrast to previous studies, which suggested they are intermediate mass ( M = 2.5–5.0 M _⊙ ) based on HR diagrams. A very high fraction of our CDGs (50%) are also Li-rich giants. We observe a bimodal distribution of luminosity in our CDGs, with one group having normal RC luminosity and the other being a factor of 2 more luminous than expected for their masses. We find demarcations in chemical patterns and luminosities, which lead us to split them into three groups: (i) normal-luminosity CDGs, (ii) overluminous CDGs, and (iii) overluminous highly polluted CDGs. We conclude that a merger of a helium white dwarf with a red giant branch star is the most likely scenario for the two groups of overluminous stars. Binary mass-transfer from intermediate-mass asymptotic giant branch stars is a possibility for the highly polluted overluminous group. For the normal-luminosity CDGs, we cannot distinguish between core He-flash pollution or lower-mass merger scenarios. Due to the overlap with the CDGs, Li-rich giants may have similar formation channels.
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