"Cats, hey. What do you do, train them?"
"Not the stuff we've got. They're no good. All but the tigers are outlaws. But I do train them."
"You like it?"
"Not much, the real big ones. But I like pumas. I'm going to get an act together with them some time. But I'll need a lot of them. Jungle pumas. Not these outlaws you see in the zoos."
"What's an outlaw?"
"He'd kill you."
"Wouldn't they all?"
"They might, but an outlaw does anyhow. If it was people, he would be a crazy person. It comes from being bred in captivity. The cats you see, they look like cats, but they're really cat lunatics."
In "The Postman Always Rings Twice", James M. Cain's hardboiled novel from 1934, cats are a continuous presence. When Frank first made a pass at her, Cora "was snarling like a cougar (10)" and when they discuss her hatred for her husband Nick she is called a hell cat. A cat's accidental suicide foils Frank and Cora's first murder attempt and after they succeed with the second murder plan their lawyer's name is Katz. But the cats in this story are the dangerous, outlaw kind.
The first cat was a true case of "curiosity killed the cat". Frank had put out a ladder as part of the plan for killing Nick, and the cat climed it but was fried by stepping on the fuse box. On some level the cat might represent the alley cat nature of Frank, but because it's referred to as "she" the cat may actually represent Cora, foreshadowing how she is later killed as the result of her association with Frank. Cora is the she-cat to Frank the tom-cat, but Frank is the outlaw kind of cat.
Madge Allen says all the cats might kill you, but the outlaw kind will. Frank is the outlaw kind. Cora believes Frank is merely a bum, but he's the wild cat born in captivity, the cat lunatic. Madge wants Frank to take a trip south with her to catch a wild puma, but that's not enough for Frank; a lunatic has no use for jungle cats because he can't convert them.
Frank is the one who first calls Cora a hell cat. He wants to believe she is like him. Cora hated her husband Nick, who called her a white bird, so the idea of being a wild hell cat appealed to her. She wanted to explore the dangerous side of life, to climb the ladder Frank had set out for her, but in the end it lead to her destruction. In the end, perhaps Nick was right; but the cat got the bird.