Frank is the baby brother Karl never had. Well, to be more accurate, Frank is the baby brother Karl may have had if he hadn't buried his real baby brother alive in a shoebox in the backyard.
Yeah, if you thought Sling Blade was a happy movie, you're quite mistaken.
When Karl was around Frank's age, his mother gave birth to a premature baby. His father asked Karl to do away with it. Karl relays the story to Frank:
KARL: I didn't know how to care for no baby. My mother and father didn't want him. They learned me to do what they told me to do. These days I figure it probably best if we just give him right back to the good Lord right off the bat anyhow.
Back then, Karl knew he couldn't take care of the baby. But now, as an adult, Karl realizes that he is able to care for Frank in a way he never could have cared for his own baby brother. In fact, Karl demonstrates his caretaker attitude when the two first meet by offering to carry Frank's laundry for him. And just like at the end of Casablanca, it's the beginning of a beautiful friendship.
Give 'Em Something to Talk About
Unlike Casablanca, though, which ends with the beginning of a friendship, Sling Blade ends with the end of one. Karl kills Doyle, ostensibly to save Frank, but in doing so he removes himself from Frank's life, much in the same way Frank's own father did.
Consider Frank's story of his father's suicide:
FRANK: You know when I told you Daddy got hit by a train? […] It ain't the truth. He shot himself with a shotgun on purpose. […] Because he didn't have enough money to take care of us the way he wanted to. That's what the letter said. […] I thought he took care of us just fine.
Frank's dad killed himself because he thought Frank would be better off that way. Karl doesn't kill himself, but he kills Doyle knowing that this means Frank will never be able to see him again afterward. Karl thinks Frank will be better off without him and Doyle, instead of with the two of them. But he never asks Frank's opinion on it. How do you think Frank feels about Karl killing Doyle?
If he and Karl were just friends, Frank might not mind so much that he's losing Karl. But they're not just friends: they're both seeking replacements for lost relatives in one another. Karl sees Frank as a little brother, while Frank sees Karl as a father figure.
However, as much as Frank might want his father back, that's never going to happen. And his fantasy of him, mom, and Karl being a family isn't going to happen, either. Sadly, Frank is a boy who has had to grow up quickly. As much as he might want to return to his innocent childhood days, that's never going to happen.
Karl is stuck in this tricky balance, too. He wants to preserve Frank's innocence, while also acknowledging his independence. So even though Karl leaves Frank, he does what Frank's own father didn't: he makes preparations for Frank. He tells Frank that he's leaving, even if he isn't completely clear about it.
KARL: Yeah, everything's gonna be all right, boy. I kind of wanna put my arm around you for a minute, then I'm gonna get up and leave out of here. I love you, boy.
Karl also gives his money to Vaughan to use to take care of Linda and Frank. Karl knows he can't deny his own nature, but he is able to be paternal to Frank in a way his own father wasn't. Before killing Doyle and returning to the mental hospital, Karl does his best to prepare Frank to live in the real world on his own. And that's what a real parent should do.