We present near-infrared observations of the low-mass deeply embedded Class 0/I system 2MASS J17112318-2724315 (2M171123) in the B59 molecular cloud. Bright scattered light nebulosity is observed toward this source in the Ks images, that seems to trace the edges of an outflow cavity. We report the detection of a low-luminosity protostar 2M17112255-27243448 (2M17112255) that lies ~8'' (~1000 AU) from 2M171123. This is a Class I system, as indicated by its 2-8 μm slope and Infrared Array Camera colors, with an estimated internal luminosity of ~0.3 L sun. We estimate a mass of ~0.12-0.25 M sun for this source, at an age of 0.1-1 Myr. Also presented is detailed modeling of the 2M171123 system. The best-fit parameters indicate a large envelope density of the order of ~10-13 g cm-3, and an intermediate inclination between 53° and 59°. The observed Ks -band variability for this system could be explained by slight variability in the mass infall rate between 2.5E-5 and 1.8E-5 M sun yr-1. The protostar 2M171123 exhibits a rarely observed absorption feature near 11.3 μm within its 10 μm silicate band. We find a strong correlation between the strength in this 11.3 μm "edge" and the H2O-ice column density, indicating the origin of this feature in the thickness of the ice mantle over the silicate grains.