The equilibrium constant and standard free energy of a reaction describe the free energy change from the Standard states of Reactants AND Products to equilibrium. Explicit in this definition is that the reaction can reach equilibrium.
At equilibrium delta G = Zero = delta H -Tdelta S. Therefore: delta H = Tdelta S. A system to reach equilibrium must have the same sign for delta H and delta S. When the signs are different the reaction must be composite or possibly a steady state but not equilibrium. Therefore, the concept of equilibrium constant does not apply.
A system with a negative deltaH and a positive entropy change might be described as a system with a positive feedback.