Herein we analyse late-time (post-plateau; 103 < t < 1229 d) optical spectra of low-redshift (z < 0.016), hydrogen-rich Type IIP supernovae (SNe IIP). Our newly constructed sample contains 91 nebular spectra of 38 SNe IIP, which is the largest dataset of its kind ever analysed in one study, and many of the objects have complementary photometric data. We determined the peak and total luminosity, velocity of the peak, HWHM intensity, and profile shape for many emission lines. Temporal evolution of these values and various flux ratios are studied. We also investigate the correlations between these measurements and photometric observables, such as the peak and plateau absolute magnitudes and the late-time light curve decline rates in various optical bands. The strongest and most robust result we find is that the luminosities of all spectral features (except those of helium) tend to be higher in objects with steeper late-time V-band decline rates. A steep late-time V-band slope likely arises from less efficient trapping of gamma-rays and positrons, which could be caused by multidimensional effects such as clumping of the ejecta or asphericity of the explosion itself. Furthermore, if gamma-rays and positrons can escape more easily, then so can photons via the observed emission lines, leading to more luminous spectral features. It is also shown that SNe IIP with larger progenitor stars have ejecta with a more physically extended oxygen layer that is well-mixed with the hydrogen layer. In addition, we find a subset of objects with evidence for asymmetric Ni-56 ejection, likely bipolar in shape. We also compare our observations to theoretical late-time spectral models of SNe IIP from two separate groups and find moderate-to-good agreement with both sets of models. Our SNe IIP spectra are consistent with models of 12-15 M_Sun progenitor stars having relatively low metallicity (Z $le$ 0.01).
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