We point out that for a range of parameters, the flux of DM may be stopped significantly by its interactions with the Earth. This can significantly degrade the sensitivity of direct detection experiments to DM candidates with large interactions with terrestrial nuclei. We find that a significant region of parameter space remains unconstrained for DM less than or similar to a few GeV. For DM candidates with moderate levels of stopping power, the flux of DM may be blocked from below but not above a detector, thereby producing a novel daily modulation. This can be explored by low threshold detectors placed on the surface or in shallow sites in the south hemisphere.