  The fate of stars in the zero-age main-sequence (ZAMS) range $\approx 8-12$
Msun is unclear. They could evolve to form white dwarfs or explode as
electron-capture supernovae (SNe) or iron core-collapse SNe (CCSNe). Even
though the initial mass function indicates that this mass range should account
for over 40% of all CCSNe progenitors, few have been observationally confirmed,
likely owing to the faintness and rapid evolution of these transients. In this
paper, we present a sample of nine Ca-rich/O-poor Type IIb SNe detected by the
Zwicky Transient Facility with progenitors likely in this mass range. We
perform a holistic analysis of the spectroscopic and photometric properties of
the sample. These sources have a flux ratio of [Ca II] $\lambda \lambda$7291,
7324 to [O I] $\lambda \lambda$6300, 6364 of $\gtrsim$ 2 in their nebular
spectra. Comparing the measured [O I] luminosity ($\lesssim 10^{39}
\mathrm{erg\ s^{-1}}$) and derived oxygen mass ($\lesssim 0.1$ Msun) with
theoretical models, we infer that the progenitor ZAMS mass for these explosions
is less than 12 Msun. These correspond to He-stars with core masses less than
around 3 Msun. We find that the ejecta properties (Mej $\lesssim 1$ Msun) are
also consistent with those expected for such low mass He-stars. The low ejecta
mass of these sources indicates a class of strongly-stripped SNe that is a
transition between the regular stripped-envelope SNe and ultra-stripped SNe.
The progenitor could be stripped by a main sequence companion and result in the
formation of a neutron star $-$ main sequence binary. Such binaries have been
suggested to be progenitors of neutron star $-$ white dwarf systems that could
merge within a Hubble time, and be detectable with LISA.
