Bound states in the continuum (BICs) of periodic lattices have been the recent focus in a variety of photonic nanostructures. Motivated by the recent results about the photons evolving in BIC structures, we investigate the quantum decay of entangled biphotons through disordered photonic lattices. We report that the persistence of bound states in disordered photonic lattices leads to an interplay between the BIC and disorder-induced Anderson localized states. We reveal a novel effect resulting from such an interplay: a nearly complete quantum survival for the entangled biphoton respecting the antisymmetric exchange symmetry. This is in contrast to the complete vanishment in a periodic photonic lattice.