Nathan said that because of David's sin, what would never depart from his house?

Answer: The sword

"The sword will never depart from your house, because you have despised Me and have taken the wife of Uriah the Hittite."

“Why then have you despised the command of the LORD by doing evil in His sight? You put Uriah the Hittite to the sword and took his wife as your own. You have slain him with the sword of the Ammonites.”— 2 Samuel 12:9 (BSB)