In most literature set in the antebellum South, all the slaves have a great fear of being sold "down the river". In Huck Finn, Jim runs away from Miss Watson because she's been talking with a slave trader, who offers her $800 for Jim, so the trader can sell Jim in New Orleans. In the far southern states, there were more large plantations, devoted to growing cotton and sugar. Working the fields was (generally) far more unpleasant that being an urban "house slave", so Jim's fear is quite rational.
My Jim is the story of Jim's wife, who is left behind when Jim runs. There's no mention of Jim's family or loved ones in Huck Finn, but Twain's overall characterization of Jim is so one-sided and stereotyped, that's not a surprise.
What is so confusing about the book is Jim is so frightened of being sold "down the river", then he and Huck raft down the river themselves, apparently somehow believing that they're heading toward Illinois. (The Mississippi River runs between Missouri - a slave state, and Illinois - a Free state. Hannibal is toward the northeast corner of Missouri. Cairo - Jim's dreamed of haven, is in the southwest part of Illinois, just south of St. Louis.) At any point, Jim and Huck could have crossed to the other side of the river and Jim would have been free.
While Illinois was a Free state by the terms of the Illinois Constitution, there was a lot of support for passing a Constitutional Amendment allowing slavery. The southern part of Illinois (where Huck and Jim were headed), was heavily in favor of the amendment. By 1850, Illinois strongly enforced the Fugitive Slave Act, which obliged northerns to help southerners recover their escaped "property."