  2002cx-like supernovae are a sub-class of sub-luminous Type Ia supernovae.
Their light curves and spectra are characterized by distinct features that
indicate strong mixing of the explosion ejecta. Pure turbulent deflagrations
have been shown to produce such mixed ejecta. Here, we present hydrodynamics,
nucleosynthesis and radiative transfer calculations for a 3D full-star
deflagration of a Chandrasekhar-mass white dwarf. Our model is able to
reproduce the characteristic observational features of SN 2005hk (a
proto-typical 2002cx-like supernova), not only in the optical, but also in the
near-infrared. For that purpose we present, for the first time, five
near-infrared spectra of SN 2005hk from -0.2 to 26.6 days with respect to
B-band maximum. Since our model burns only small parts of the initial white
dwarf, it fails to completely unbind the white dwarf and leaves behind a bound
remnant of ~1.03 solar masses -- consisting mainly of unburned carbon and
oxygen, but also enriched by some amount of intermediate-mass and iron-group
elements from the explosion products that fall back on the remnant. We discuss
possibilities for detecting this bound remnant and how it might influence the
late-time observables of 2002cx-like SNe.
