The fate of stars in the zero-age main-sequence (ZAMS) range ≈8–12 M_⊙ 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 CCSN progenitors, few have been observationally confirmed, likely due to the faintness and rapid evolution of some 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. These sources have a [Ca ii] λλ7291, 7324/[O i] λλ6300, 6364 flux ratio of ≳2 in their nebular spectra. Comparing the measured [O i] luminosity (≲10³⁹ erg s⁻¹) and derived oxygen mass (≈0.01 M_⊙) with theoretical models, we infer that the progenitor ZAMS mass for these explosions is less than 12 M_⊙. The ejecta properties (M_ej ≲ 1 M_⊙ and E_kin ∼ 10⁵⁰ erg) are also consistent. 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.