We explore the idea of a network of domain walls appearing on the surface o
f a soliton star. We show that for a suitable fine-tuning among the paramet
ers of the model we can find localized fermion zero modes only on the netwo
rk of domain walls. In this scenario. the soliton star becomes unstable and
decays into free particles before the cold-matter upper mass limit is achi
eved. However, if fermions do not bind to the network of domain walls, the
network becomes neutral. imposing a new lower bound on the charge of the so
liton star, slightly raising its critical mass.