  We present nebular-phase spectra of the Type Ia supernova (SN Ia) 2016brx, a
member of the 1991bg-like subclass that lies at the faint end of the SN Ia
luminosity function. Nebular spectra are available for only three other
1991bg-like SNe, and their Co line centers are all within <~ 500 km/s of each
other. In contrast, the nebular Co line center of SN 2016brx is blue-shifted by
>1500 km/s compared to them and by ~1200 km/s compared to the rest frame. This
is a significant shift relative to the narrow nebular line velocity dispersion
of <~ 2000 km/s of these SNe. The large range of nebular line shifts implies
that the Ni56 in the ejecta of SN 1991bg-like events is off-center by ~1000
km/s rather than universally centrally confined as previously suggested. With
the addition of SN 2016brx, the Co nebular line shapes of 1991bg-like objects
appear to connect with the brighter SNe Ia that show double-peak profiles,
hinting at a continuous distribution of line profiles among SNe Ia. One class
of models to produce both off-center and bi-modal Ni56 distributions is
collisions of white dwarfs with unequal and equal masses.
