Regular tap water contains very little sodium. The amount of sodium a water softener adds to tap water depends on the "hardness" of the water. Hard water contains large amounts of calcium and magnesium. Some water-softening systems replace calcium and magnesium ions with sodium ions. The higher the concentration of calcium and magnesium, the more sodium needed to soften the water. Even so, the added sodium doesn't add up to much.
An 8-ounce (237-milliliter) glass of softened water generally contains less than 12.5 milligrams of sodium, which is well within the Food and Drug Administration's definition of "very low sodium." Thus, it's unlikely that sodium in softened water would pose a risk for most healthy people.
However, if you're on a very low-sodium diet and you're concerned about the amount of sodium in softened water, you may want to consider a water-purification system that uses potassium chloride instead. Another option is to soften only the hot water and use unsoftened cold water for drinking and cooking.
In any case, it's important to keep in mind that the majority of sodium in an average person's diet comes from table salt and processed foods. Thus, the best way to decrease sodium in your diet is by putting away the saltshaker and cutting back on processed foods.