“火中取栗”is a well-known idiom story in China which means gain profits in risk, especially when the action only profits another people. Literally, “火” means fire, “取” means pull, “栗” means chestnut. When these words join together, it means “pull a chestnut out of fire”. How does this idiom come into being? Here is an interesting story.
A long time ago, there was a forest in which only animals lived there. One day, a monkey saw a chestnut in a fire. The chestnut was given its fragrance in the open fire, and the smell was so pleasant that the monkey couldn't help drool. He wanted to eat it, but it was too hot to pull the chestnut out of the fire.
Just at that time, a cat passed by. “Come here!” the monkey shouted. And then he induced the cat to pick the chestnut out and ate it immediately. The cat got nothing except the hair on its paw was burnt.
So, this idiom “Be a cat’s paw”, refers to those who take risks for others without even knowing it.