  The Baryon Oscillation Spectroscopic Survey (BOSS) has collected spectra for
over one million galaxies at $0.15<z<0.7$ over a volume of 15.3 Gpc$^3$ (9,376
deg$^2$) -- providing us an opportunity to study the most massive galaxy
populations with vanishing sample variance. However, BOSS samples are selected
via complex color cuts that are optimized for cosmology studies, not galaxy
science. In this paper, we supplement BOSS samples with photometric redshifts
from the Stripe 82 Massive Galaxy Catalog and measure the total galaxy stellar
mass function (SMF) at $z\sim0.3$ and $z\sim0.55$. With the total SMF in hand,
we characterize the stellar mass completeness of BOSS samples. The
high-redshift CMASS ("constant mass") sample is significantly impacted by mass
incompleteness and is 80% complete at $\log_{10}(M_*/M_{\odot}) >11.6$ only in
the narrow redshift range $z=[0.51,0.61]$. The low redshift LOWZ sample is 80%
complete at $\log_{10}(M_*/M_{\odot}) >11.6$ for $z=[0.15,0.43]$. To construct
mass complete samples at lower masses, spectroscopic samples need to be
significantly supplemented by photometric redshifts. This work will enable
future studies to better utilize the BOSS samples for galaxy-formation science.
