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Since the Sanitation Services Inc employed by the slaughterhouses got fined for this, Arkansas under Huckabee signed a law removing requirements to verify ages of anyone working under 16. Aka no one is liable if children are working in slaughterhouses and getting chemical burns.
Here's a picture of one of the kids.
Liable for hiring children, I thought the OP meant.
But there is an issue with liability for injury. Securing a legal remedy requires knowing one's rights, knowing how to express those rights, and knowing how to start the litigation process. Children are unlikely to know any of these, considering most adults don't, either. And a state that allows child labour is unlikely to set up any mechanisms to provide that knowledge or make the litigation procedure easier to navigate. So even if the employer could technically be liable for workplace injuries, the chances of being sued successfully are slim.