How does Katherine Paterson's analogy comparing Lyddie to a “slave” interact with other text elements and contribute to the over all plot?

Though she was never a slave, Lyddie is certainly treated like one at various points in the story. She has to work on behalf of her family after her father walks out on them and after her mother is put away in an institution. Her first port of call in the big, scary world outside is Cutler's Tavern. Here, Lyddie is forced to put in sixteen-hour days, which are as soul-destroying as they are back-breaking. This isn't slavery, but it's the nearest thing to it that a white person at the time would've experienced.
Then, when Lyddie's had enough of the tavern, she rocks up at a factory in Concord. Life here is pretty tough. Pay is low, hours are long, and the conditions are dangerous. Throw in a sex-pest supervisor, and it's not a place where anyone would work if they had the choice. But Lyddie has no choice, and so she works at the factory, very very hard. Her experiences there are crucial to the plot because they allow Lyddie to develop and mature as a young woman and give her the opportunity to help out her family.