Jim is suspected of having killed Huck Finn. However, Jim turns out to be a character who deeply cares for Huck's well-being. When Huck and Jim first meet on Jackson Island (and Huck explains the story of how he got there), Jim explains:
I 'uz powerful sorry you's killed Huck, but I ain't no mo' now.
From the beginning of the novel, Jim shows kindness and compassion toward Huck. He is his friend, and he grows closer to him throughout the story.
In chapter 11, Huck dresses like a girl (calling himself "Sarah Williams") and goes into town from Jackson Island to find out news. The woman (Mrs. Judith Loftus) begins to tell Huck stories about "Huck's death" (which never really happened), and she explains that some people think that his Pap (his father) killed him:
Some think old Finn done it himself. . . . Most everybody thought it at first. He'll never know how nigh he come to getting lynched. But before night they changed around and judged it was done by a runaway nigger named Jim.
This information, that Jim is now suspected of killing him, alarms Huck, and he almost gives away that he knows more information than a stranger in town should. However, he stops himself from speaking and listens to her story.
She explains that they suspect Jim is guilty of the crime because he ran off the same night that Huck was supposedly killed. There is a $300 reward for anyone who turns Jim in; there is a $200 reward for Pap. This reward is biased and unfair. There is little to no evidence (other than timing) that Jim harmed Huck. However, the reward for turning him in is more (probably because of his skin color and status as a slave) than it is for Huck's white dad, who was known to be a drunk and an abusive father.