I couldn't imagine why anyone would supplement with sodium. We do so much "supplementation" already with our salt shakers. All that shaking is linked to hypertension, but overall, when food is salted lightly, the salting may not be all bad.
When you eat salt, it guards you against sodium deficiency. The deficiency is not as likely now, but in earlier days it may have been an issue and continues to be a problem with anorexia.(1) The deficiency's symptoms include nausea, muscle atrophy, poor growth and weight loss.(1p380)
Plus, if the salt is iodized, then it helps guard against iodine deficiency. Iodine is extremely variable in foods so having it as part of salt is beneficial.(1p468) The thyroid collects the iodine, in its ionic form iodide, and uses it for genesis of hormones.(1p418)
1. Gropper, S.S., Smith, J.L. & Groff, J.L. Advanced Nutrition and Human Metabolism, 4th ed; 2005. Belmont, CA: Thomson Wadsworth.