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The prison turnkey (the guy who keeps an eye on the prison door, basically) becomes Little Dorrit's godfather, and they are very close. He takes her on walks outside the prison.
Sometimes she asks him questions about what life is like outside the prison and what people who aren't prisoners do. He doesn't know what to say and gives her treats as a distraction.
The turnkey wants to leave money just to her in his will, but there is no way to "tie it up" so that no one but Little Dorrit can touch it, so he dies without a will.
Little Dorrit is the only member of the family who can take the long view of things and try to see what's going on with the Dorrits from the outside.
She takes it upon herself to get her brother and sister educated.
Little Dorrit asks an imprisoned dancing master to teach her sister to dance, and that goes well.
She herself learns to sew and embroider from an imprisoned milliner (hat-maker).
While all this is happening, Mr. Dorrit starts to believe his whole I-was-a-fancy-gentleman shtick. He starts crying every time someone mentions that his kids work for a living – for two reasons: 1) gentlemen and their families don't work, and 2) obviously if anyone should be working, it should be him.
So Little Dorrit decides to start pretending they don't work and are instead going out to party all day. Seriously. And Mr. Dorrit decides to not only buy it, but also to sort of scold them for doing so much all-day partying.
Fanny becomes a dancer and goes to live with Mr. Dorrit's brother Frederick. Good-old Fred is also completely poor because of Mr. Dorrit's bankruptcy, and was so shocked by this calamity that he has completely stopped washing himself or his clothes. He is a clarinet player in the little theater where Fanny dances.
It might be a helpful brain snack to mention here that back then, being a dancer was one – maybe two – steps up from being a prostitute. Fanny's big hope would have been to become some rich dude's kept woman. So yeah – no great shakes.
Brother Tip is hardest to deal with. He has already become a semi-pro conman and small-time riffraff when Little Dorrit tries to get him into a variety of trades. He quits all of them and comes back to the prison. Finally one day he comes back and tells her that this time he's "off the volunteer list altogether. [He is] in now, as one of the regulars" for a big debt (1.7.98).
Little Dorrit loses it, but they all decide to lie about it to Daddy Dorrit, to spare his feelings.