We study a model in which two scenarios for eventual mixing of stratified flows (shearinstability and internal breaking waves) are, in principle, possible. In this shallow water two-layer flow model it is found that unforced flows cannot reach the threshold of shearinstability without breaking first. Mathematically, for 2X2 autonomous systems of mixed type, a criterium is found deciding whether the elliptic domain is reachable from hyperbolic initial conditions.