  We analyze two binary systems containing giant stars, V723 Mon ("the
Unicorn") and 2M04123153+6738486 ("the Giraffe"). Both giants orbit more
massive but less luminous companions, previously proposed to be mass-gap black
holes. Spectral disentangling reveals luminous companions with star-like
spectra in both systems. Joint modeling of the spectra, light curves, and
spectral energy distributions robustly constrains the masses, temperatures, and
radii of both components: the primaries are luminous, cool giants ($T_{\rm
eff,\,giant} = 3,800\,\rm K$ and $4,000\,\rm K$, $R_{\rm giant}=
22.5\,R_{\odot}$ and $25\,R_{\odot}$) with exceptionally low masses ($M_{\rm
giant} \approx 0.4\,M_{\odot}$) that likely fill their Roche lobes. The
secondaries are only slightly warmer subgiants ($T_{\rm eff,\,2} = 5,800\,\rm
K$ and $5,150\,\rm K$, $R_2= 8.3\,R_{\odot}$ and $9\,R_{\odot}$) and thus are
consistent with observed UV limits that would rule out main-sequence stars with
similar masses ($M_2 \approx 2.8\,M_{\odot}$ and $\approx 1.8\,M_{\odot}$). In
the Unicorn, rapid rotation blurs the spectral lines of the subgiant, making it
challenging to detect even at wavelengths where it dominates the total light.
Both giants have surface abundances indicative of CNO processing and subsequent
envelope stripping. The properties of both systems can be reproduced by binary
evolution models in which a $1-2\,M_{\odot}$ primary is stripped by a companion
as it ascends the giant branch. The fact that the companions are also evolved
implies either that the initial mass ratio was very near unity, or that the
companions are temporarily inflated due to rapid accretion. The Unicorn and
Giraffe offer a window into into a rarely-observed phase of binary evolution
preceding the formation of wide-orbit helium white dwarfs, and eventually,
compact binaries containing two helium white dwarfs.
