We present nebular spectroscopy of SN 2020hvf, a Type Ia supernova (SN Ia) with an early bump in its light curve. SN 2020hvf shares many spectroscopic and photometric similarities to the carbon-rich high-luminosity “03fg-like” SNe Ia. At >240 days after peak brightness, we detect unambiguous emission from [Ca ii] λ
λ7291, 7324, which is rarely observed in normal SNe Ia and only seen in peculiar subclasses. SN 2020hvf displays “sawtooth” emission profiles near 7300 Å that cannot be explained with single symmetric velocity components of [Fe ii], [Ni ii], and [Ca ii], indicating an asymmetric explosion. The broad [Ca ii] emission is best modeled by two velocity components offset by 1220 km s−1, which could be caused by ejecta associated with each star in the progenitor system, separated by their orbital velocity. For the first time in an SN Ia, we identify narrow (FWHM = 180 ± 40 km s−1) [Ca ii] emission, which we associate with a wind from a surviving, puffed-up companion star. Few published spectra have sufficient resolution and the signal-to-noise ratio necessary to detect similar narrow [Ca ii] emission; however, we have detected similar line profiles in other 03fg-like SNe Ia. The extremely narrow velocity width of [Ca ii] has only otherwise been observed in SNe Iax at late times. Since this event likely had a double-degenerate “super-Chandrasekhar” mass progenitor system, we suggest that a single white dwarf (WD) was fully disrupted and a wind from a surviving companion WD is producing the observed narrow emission. It is unclear whether this unique progenitor and explosion scenario can explain the diversity of 03fg-like SNe Ia, potentially indicating that multiple progenitor channels contribute to this subclass.