We find type I critical collapses of compact objects modeled by a polytropic equation of state (EOS) with a polytropic index Gamma=2 without the ultrarelativistic assumption. The object is formed in head-on collisions of neutron stars. Further, we show that the critical collapse can occur due to a change of the EOS, without fine-tuning of initial data. This opens the possibility that a neutron-star-like compact object, not just those formed in a collision, may undergo a critical collapse in processes which slowly change the EOS, such as cooling.