According to Appendix A of
LotR, after the death of his last surviving son:
Helm grew fierce and gaunt for famine and grief, and the dread of him alone was worth many men in the defence of the Burg. He would go out by himself, clad in white, and stalk like a snow-troll into the camps of his enemies, and slay many men with his hands. It was believed that if he bore no weapon no weapon would bite on him. The Dunlendings said that if he could find no food he ate men. That tale lasted long in Dunland.
I agree with you,
Morthoron, that Dunlending mothers would calm down their children with that admonition; but they would also make very clear that Helm
ate naughty children.