The edge energy of the 2-dimensional electron gas with high density is calculated, here the edge energy implies the energy which is needed to form a unit length of new edge when a 2-dimensional infinite homogeneous electron system is cleft into two pieces of semi-infinite electron systems. It is found that, for rss(c)≈0.415, the edge energy becomes negative, indicating that at high enough density the ground state of the 2-dimensional electron gas can be unstable. The stability of the ground state of the bound and unbound 2-dimensional electron gas is discussed and a criterion for the ground-state stability of the bound 2-dimensional electron gas is obtained for a simplified model.