Nebular-phase observations and spectral models of Type Ic superluminous supernovae (SLSNe) are presented. LSQ14an and SN 2015bn both display late-time spectra similar to galaxy-subtracted spectra of SN 2007bi, and the class shows strong similarity with broad-lined SNe Ic such as SN 1998bw. Near-infrared observations of SN 2015bn show a strong Ca $II$ triplet, O $I$ 9263, O $I$ 1.13 μm, and Mg $I$ 1.50 μm, but no distinct He, Si, or S emission. The high Ca $II$ NIR/[Ca $II$] 7291, 7323 ratio of ~2 indicates a high electron density of $ne$ $\gtrsim$ 10$8$ cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-3</mrow>}$. Spectral models of oxygen-zone emission are investigated to put constraints on the emitting region. Models require $M$ (O-zone) $\gtrsim$ 10 $M\odot$ to produce enough [O $I$] 6300, 6364 luminosity, irrespective of the powering situation and the density. The high oxygen-zone mass, supported by high estimated magnesium masses, points to explosions of massive CO cores, requiring $MZAMS$ $\gtrsim$ 40 $M\odot$. Collisions of pair-instability pulsations do not provide enough mass to account for the emission. [O $II$] and [O $III$] lines emerge naturally in many models, which strengthens the identification of broad [O $II$] 7320, 7330, [O $III$] 4363, and [O $III$] 4959, 5007 in some spectra. A small filling factor $f$ $\lesssim$ 0.01 for the O/Mg zone is needed to produce enough luminosity in Mg $I$] 4571, Mg $I$ 1.504 μm, and O $I$ recombination lines, which shows that the ejecta is clumped. We review the constraints from the nebular spectral modeling in the context of the various scenarios proposed for SLSNe.