We present multi-wavelength follow-up observations of the ATLAS discovered faint Iax supernova SN 2020kyg (ATLAS20nuc) discovered in NGC 5012 at ∼ 40 Mpc. SN 2020kyg peaked at an absolute magnitude of 𝑀 𝑔 ≈ −14.9 ± 0.2, making it another member of the faint Iax supernova population. The bolometric light curve is adequately fit with an Arnett model, requiring only ≈ 7 × 10 −3 M of radioactive 56 Ni, with an ejected mass of 𝑀 ej ∼ 0.4 M . The 𝑔-band rise time inferred from the fit is ∼ 10 days, consistent with the low luminosity. The photospheric velocity around maximum, deduced from Si 𝜆6355 is ∼ 4500 km s −1 implying a low kinetic energy of 𝐸 51 ≈ 0.05 ± 0.02 erg. A self-consistent model constructed using the 1D radiative transfer code for the early optical spectra is dominated by carbon, oxygen, neon and intermediate mass elements like silicon, sulphur and magnesium. The model deviates significantly from the observed spectrum at > +14 days, suggesting the ejecta is transitioning towards an optically thin state, and/or presence of significant radioactive material in the outer layers of the ejecta. In order to constrain the rates of SNe Iax in the local Universe, we construct a homogeneous volume-limited sample of 902 transients observed by ATLAS within 100 Mpc during a 3.5 year span. Using this sample, we constrain the rates of faint Iax (𝑀 𝑟 −16) events within 60 Mpc at 12 +13 −8 % of the SN Ia rate. The overall Iax rate, at 15 +15 −9 % of the Ia rate, is dominated by the low-luminosity events, with luminous SNe Iax (𝑀 𝑟 −17.5) like 2002cx and 2005hk accounting for less than 1% of the Ia rate. We favor the hybrid CONe WD + He star progenitor channel involving a failed deflagration of a near Chandrasekhar mass white dwarf, expected to leave a bound remnant and a surviving secondary companion, as a candidate explanation for faint Iax explosions. This scenario requires short delay times, consistent with the observed environments of SNe Iax. Furthermore, binary population synthesis calculations have suggested rates of 1 − 18% of the SN Ia rate for this channel, consistent with our rate estimates.