We modeled the subsurface transport of H₂O and CO₂ on Mars in a two-dimensional pole-to-equator cross-section, starting with sudden surface freezing representing ancient climate change. We find that excursions to low obliquity strongly drive ice sublimation and subsequent groundwater evaporation at low latitudes. This creates a hydraulic gradient in the saturated zone that moves water equatorward and even sublimates the base of high-latitude ice. Eventually, all H₂O is lost at latitudes less than ∼30°. A subcryospheric vadose zone may be retained at higher latitudes, but ultimately only a few monolayers of adsorbed water will be held. A subcryospheric phreatic zone is preserved in the same regions only where lateral heterogeneity restricts horizontal fluid flow. The predicted contemporary state of Mars is drier and with groundwater—if present at all—in different locations than previously considered.