This paper introduces the concept of “robust survival” as a sufficient condition for the existence of equilibrium in a general equilibrium model with incomplete markets (GEI). The robust survival condition is weaker than the GEI irreducibility condition proposed by Gottardi and Hens (1996) in the GEI model, and it is less affected by the degree of market incompleteness. Unlike the GEI irreducibility condition of Gottardi and Hens (1996), the robust survival condition provides an explanation for the existence of a GEI equilibrium in which an agent can consume with the minimum expenditure on feasible consumptions. This condition can be used to evaluate the impact of financial innovation on the welfare of the poor. When an economy passes the robust survival condition but fails the GEI irreducibility condition, some agents may be “poor” in pre-innovation equilibrium. In this case, we can apply the GEI irreducibility condition to the post-innovation economy to determine whether financial innovation makes the invisible hand benevolent towards the poor.