We present and analyze a near-infrared (NIR) spectrum of the underluminous Type Ia supernova SN 2020qxp/ASASSN-20jq obtained with NIRES at the Keck Observatory, 191 days after B-band maximum. The spectrum is dominated by a number of broad emission features, including the [FeII] at 1.644{mu}m, which is highly asymmetric with a tilted top and a peak redshifted by ~2000km/s. In comparison with 2D non-LTE synthetic spectra computed from 3D simulations of off-center delayed-detonation Chandrasekhar-mass (M_ch_) white dwarf (WD) models, we find good agreement between the observed lines and the synthetic profiles, and are able to unravel the structure of the progenitor's envelope. We find that the size and tilt of the [FeII]1.644{mu}m profile (in velocity space) is an effective way to determine the location of an off-center delayed-detonation transition (DDT) and the viewing angle, and it requires a WD with a high central density of ~4x10^9^g/cm^3^. We also tentatively identify a stable Ni feature around 1.9{mu}m characterized by a "pot-belly" profile that is slightly offset with respect to the kinematic center. In the case of SN 2020qxp/ASASSN-20jq, we estimate that the location of the DDT is ~0.3M_WD_ off center, which gives rise to an asymmetric distribution of the underlying ejecta. We also demonstrate that low-luminosity and high-density WD SN Ia progenitors exhibit a very strong overlap of Ca and ^56^Ni in physical space. This results in the formation of a prevalent [CaII]0.73{mu}m emission feature that is sensitive to asymmetry effects. Our findings are discussed within the context of alternative scenarios, including off-center C/O detonations in He-triggered sub-M_Ch_ WDs and the direct collision of two WDs. Snapshot programs with Gemini/Keck/Very Large Telescope (VLT)/ELT-class instruments and our spectropolarimetry program are complementary to mid-IR spectra by the James Webb Space Telescope (JWST).