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Wide-field near-infrared (NIR) polarimetry was used to examine disk systems around two brown dwarfs (BDs) and two young stellar objects (YSOs) embedded in the Heiles Cloud 2 (HCl2) dark molecular cloud in Taurus as well as numerous stars located behind HCl2. Inclined disks exhibit intrinsic NIR polarization due to scattering of photospheric light, which is detectable even for unresolved systems. After removing polarization contributions from magnetically aligned dust in HCl2 determined from the background star information, significant intrinsic polarization was detected from the disk systems of one BD (ITG 17) and both YSOs (ITG 15, ITG 25), but not from the other BD (2M0444). The ITG 17 BD shows good agreement of the disk orientation inferred from the NIR and from published Atacama Large Millimeter/submillieter Array dust continuum imaging. ITG 17 was also found to reside in a 5200 au wide binary (or hierarchical quad star system) with the ITG 15 YSO disk system. The inferred disk orientations from the NIR for ITG 15 and ITG 17 are parallel to each other and perpendicular to the local magnetic field direction. The multiplicity of the system and the large BD disk nature could have resulted from formation in an environment characterized by misalignment of the magnetic field and the protostellar disks.