The objective of the Phoenix mission is to determine if Mars' polar region can support life. Since liquid water is a basic ingredient for life, as we know it, an important goal of the mission is to determine if liquid water exists at the landing site. It is believed that a layer of Martian soil preserves ice by forming a barrier against high temperatures and sublimation, but that exposed ice sublimates without the formation of the liquid phase. Here we show possible independent physical and thermodynamical evidence that besides ice, liquid saline water exists in areas disturbed by the Phoenix Lander. Moreover, we show that the thermodynamics of freeze-thaw cycles can lead to the formation of saline solutions with freezing temperatures lower than current summer ground temperatures on the Phoenix landing site on Mars' Arctic. Thus, we hypothesize that liquid saline water might occur where ground ice exists near the Martian surface. The ideas and results presented in this article provide significant new insights into the behavior of water on Mars.