Mean-field dynamics of strongly interacting bosons described by hard-core bosons with nearest-neighbor attraction has been shown to support two species of solitons: one of Gross-Pitaevskii type (GP type) where the condensate fraction remains dark, and a non-Gross-Pitaevskii type (non-GP type) characterized by brightening of the condensate fraction. Here we study the effects of quantum fluctuations on these solitons using the adaptive time-dependent density matrix renormalization group method, which takes into account the effect of strong correlations. We use local observables as the density, condensate density, and correlation functions as well as the entanglement entropy to characterize the stability of the initial states. We find both species of solitons to be stable under quantum evolution for a finite duration, their tolerance to quantum fluctuations being enhanced as the width of the soliton increases. We describe possible experimental realizations in atomic Bose-Einstein condensates, polarized degenerate Fermi gases, and in systems of polar molecules on optical lattices.