  The initial-final mass relation (IFMR) represents the total mass lost by a
star during the entirety of its evolution from the zero age main sequence to
the white dwarf cooling track. The semi-empirical IFMR is largely based on
observations of DA white dwarfs, the most common spectral type of white dwarf
and the simplest atmosphere to model. We present a first derivation of the
semi-empirical IFMR for hydrogen deficient white dwarfs (non-DA) in open star
clusters. We identify a possible discrepancy between the DA and non-DA IFMRs,
with non-DA white dwarfs $\approx 0.07 M_\odot$ less massive at a given initial
mass. Such a discrepancy is unexpected based on theoretical models of non-DA
formation and observations of field white dwarf mass distributions. If real,
the discrepancy is likely due to enhanced mass loss during the final thermal
pulse and renewed post-AGB evolution of the star. However, we are dubious that
the mass discrepancy is physical and instead is due to the small sample size,
to systematic issues in model atmospheres of non-DAs, and to the uncertain
evolutionary history of Procyon B (spectral type DQZ). A significantly larger
sample size is needed to test these assertions. In addition, we also present
Monte Carlo models of the correlated errors for DA and non-DA white dwarfs in
the initial-final mass plane. We find the uncertainties in initial-final mass
determinations for individual white dwarfs can be significantly asymmetric, but
the recovered functional form of the IFMR is grossly unaffected by the
correlated errors.
