Can my boss pay for me if I get sued while working for him?

Question Details: Let's say that my new boss wanted me to sign a contract that states that I'm responsible for my own insurances and accidents. However, is there a law or contract that could protect me from getting sued while working for him? For example, if I was a hairstylist and I accidentally cut their ear and they wanted to sue. Is there a law that says the boss has to pay instead because we are his workers?

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