Excess sodium is absorbed from the blood and excreted by the kidneys, which help regulate many body systems. High sodium levels thus have the potential for having indirect effects on those systems. There’s evidence that they can cause loss of bone calcium and thus increase our dietary calcium requirement, as well as worsening chronic kidney disease.
Though our bodies have ways of diluting and excreting excessive doses of salt, eating salty foods exposes the surfaces of our digestive system to potentially cell-damaging concentrations. There is evidence from China and elsewhere in Asia that diets high in salt increase the risk of several cancers of the digestive system.