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Doyce takes Arthur to Bleeding Heart Yard, home of Doyce's factory, where Little Dorrit's friend Plornish also happens to live. (As always with Dickens, the huge metropolis of London turns out to be a small world.)
Arthur looks for Plornish's house and finds Mrs. Plornish and a couple of kids. They're waiting for Plornish to come back from looking for work.
Turns out that the Plornishes are part of the working poor. All Mr. Plornish ever does is look for work, but still they are living hand to mouth.
(Brain snacktacular: this is a dig at the political economists of the day – check out the "In a Nutshell" section for some info on that. The basic line back in the day, and sometimes still nowadays, was that poor people are just lazy; if they worked, they wouldn't be poor. Dickens always liked to point out that that's a pretty simplistic view of the situation.)
Plornish comes home and at first is suspicious that Arthur is some kind of debt collector.
But then they get all BFF when Arthur explains that he's Little Dorrit's friend.
The Plornishes are psyched to know Dorrit, and they brag about the size of his debts. They buy the whole I-used-to-be-a-gentleman story.
Arthur is still doing his investigation of his mom and asks how Plornish introduced Little Dorrit to Mrs. Clennam.
Plornish tells him about Little Dorrit's ads for doing needlework. One of these went to Mr. Casby, who's the landlord of Bleeding Heart Yard – and through him, Mrs. Clennam found Little Dorrit.
Arthur is all, "Oh, wait, I know Mr. Casby!" – again, proving the small world theory. Yeesh.
Anyhoodle, Plornish helps Arthur settle Tip Dorrit's imprisoning debt for pennies on the dollar.
Arthur drops him off at the Marshalsea to tell Tip he's free to go but makes Plornish promise to keep it a secret how the debt was settled.
They also totally pinkie-swear to do good things for Little Dorrit whenever they can.