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.