  We present a comprehensive dataset of optical and near-infrared photometry
and spectroscopy of type~Ia supernova (SN) 2016hnk, combined with integral
field spectroscopy (IFS) of its host galaxy, MCG -01-06-070, and nearby
environment. Properties of the SN local environment are characterized by means
of single stellar population synthesis applied to IFS observations taken two
years after the SN exploded. SN 2016hnk spectra are compared to other
1991bg-like SNe Ia, 2002es-like SNe Ia, and Ca-rich transients. In addition,
abundance stratification modelling is used to identify the various spectral
features in the early phase spectral sequence and the dataset is also compared
to a modified non-LTE model previously produced for the sublumnious SN 1999by.
SN 2016hnk is consistent with being a sub-luminous (M$_{\rm B}=-16.7$ mag,
s$_{\rm BV}$=0.43$\pm$0.03), highly reddened object. IFS of its host galaxy
reveals both a significant amount of dust at the SN location, as well as
residual star formation and a high proportion of old stellar populations in the
local environment compared to other locations in the galaxy, which favours an
old progenitor for SN 2016hnk. Inspection of a nebular spectrum obtained one
year after maximum contains two narrow emission lines attributed to the
forbidden [Ca II] $\lambda\lambda$7291,7324 doublet with a Doppler shift of 700
km s$^{-1}$. Based on various observational diagnostics, we argue that the
progenitor of SN 2016hnk was likely a near Chandrasekhar-mass ($M_{\rm Ch}$)
carbon-oxygen white dwarf that produced 0.108 $M_\odot$ of $^{56}$Ni. Our
modeling suggests that the narrow [Ca II] features observed in the nebular
spectrum are associated with $^{48}$Ca from electron capture during the
explosion, which is expected to occur only in white dwarfs that explode near or
at the $M_{\rm Ch}$ limit.
