Nuclei are nearly transparent to each other when they collide at high energy, but the collisions do produce high-energy density matter in the central rapidity region where most experimental measurements are made. What happens to the receding nuclear fireballs? We calculate the energy loss of the nuclei using the color glass condensate model. We then use a simple space-time picture of the collision to calculate the baryon and energy densities of the receding fireballs. For central collisions of large nuclei at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider we find baryon densities more than ten times that of normal nuclear matter. These results provide initial conditions for subsequent hydrodynamic evolution and could test the equation of state at very high baryon densities.