We present the first J-band spectrum of Mrk 231, which reveals a large He I {lambda}10830 broad absorption line with a profile similar to that of the well-known Na I broad absorption line. Combining this spectrum with optical and UV spectra from the literature, we show that the unusual reddening noted by Veilleux et al. (2013ApJ...764...15V) is explained by a reddening curve like those previously used to explain low values of total-to-selective extinction in Type Ia supernovae. The nuclear starburst may be the origin and location of the dust. Spatially resolved emission in the broad absorption line trough suggests nearly full coverage of the continuum emission region. The broad absorption lines reveal higher velocities in the He I lines (produced in the quasar-photoionized H II region) compared with the Na I and Ca II lines (produced in the corresponding partially ionized zone). Cloudy simulations show that a density increase is required between the H II and partially ionized zones to produce ionic column densities consistent with the optical and IR absorption line measurements and limits, and that the absorber lies ~100 pc from the central engine. These results suggest that the He I* lines are produced in an ordinary quasar BAL wind that impacts upon, compresses, and accelerates the nuclear starburst's dusty effluent (feedback in action), and the Ca II and Na I lines are produced in this dusty accelerated gas. This unusual circumstance explains the rarity of Na I absorption lines; without the compression along our line of sight, Mrk 231 would appear as an ordinary iron low-ionization, broad absorption line quasar.