Recent studies have argued that the progenitor system of type Iax supernovae must consist of a carbon-oxygen white dwarf accreting from a helium star companion. Based on existing explosion models invoking the pure deflagration of carbon-oxygen white dwarfs, we investigate the likelihood of producing spectral features due to helium in type Iax supernovae. From this scenario, we select those explosion models producing ejecta and $^{56}$Ni masses that are broadly consistent with those estimated for type Iax supernovae (0.014 - 0.478~$M_{odot}$ and $sim0.003$ - 0.183~$M_{odot}$, respectively). To this end, we present a series of models of varying luminosities ($-18.4 lesssim M_{rm{V}} lesssim -14.5$~mag) with helium abundances accounting for up to $sim$36% of the ejecta mass, and covering a range of epochs beginning a few days before B$-$band maximum to approximately two weeks after maximum. We find that the best opportunity for detecting ion{He}{i} features is at near-infrared wavelengths, and in the post-maximum spectra of the fainter members of this class. We show that the optical spectrum of SN~2007J is potentially consistent with a large helium content (a few 10$^{-2}~M_{odot}$), but argue that current models of accretion and material stripping from a companion struggle to produce compatible scenarios. We also investigate the presence of helium in all objects with near-infrared spectra. We show that SNe~2005hk, 2012Z, and 2015H contain either no helium or their helium abundances are constrained to much lower values ($lesssim$10$^{-3}~M_{odot}$). Our results demonstrate the differences in helium content among type Iax supernovae, perhaps pointing to different progenitor channels. Either SN~2007J is an outlier in terms of its progenitor system, or it is not a true member of the type Iax supernova class.
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