While the whole novel is built around justice for those downtrodden by society, there are five specific examples of poverty that Victor Hugo focuses on in Les Misérables:
Fantine is completely screwed over by the system, partly because options are fewer for women than men, and partly because of the stigma against unwed mothers. Ultimately she ends up in the most degrading profession she can imagine, and dies from inadequate health care.
Marius, after falling out with his grandfather, chooses to take no money he hasn’t earned, and doesn’t earn very much. But he’s got options: he’s in school, and he has at least somewhat marketable skills, and of course there’s no stigma against young men. Plus he has a support network so he can crash at a friend’s apartment, or split the cost of the occasional social meal. He scrapes by in a crappy apartment until he earns his degree, but even then, he can’t quite pull himself out by himself, and it’s only after he (a) meets Cosette, who has money and (b) reconciles with his wealthy grandfather and moves back in with him that he’s able to enjoy a higher standard of living.
The Thénardiers, after they lose their inn, are in desperate straits, but rather than trying to scrape by, they do what they’ve always done: prey on society. They don’t seem to be very good at it, and while it’s hard to have any pity for the parents, it’s painful to read about how Éponine and Azelma live.
Gavroche, a child living on the streets. Of course, a child can get away with breaking a lot more rules than an adult can, and Gavroche is so optimistic he almost doesn’t care. Almost.
Finally, Pere Mabeuf, Marius’ friend who lives a modest but comfortable life off a book he published when he was younger, but as his work falls out of demand and he ages out of the job market, he is effectively done in by the lack of support for the elderly. Technically it’s a bullet that kills him, but he only ends up at the barricade because he’s reached the end of his rope and starts walking.
There are others: Valjean’s distant past (his role in the novel deals more with the flaws in the justice system than with economic class*), the voluntary austerity of Bishop Myriel and the nuns at the convent, the Thénardiers’ Parisian associates, and of course many nameless background characters, but these are the lives we get to see up close.
*It’s worth mentioning that as M. Madeleine, Jean Valjean is the only self-made man in the novel…and even he needed some seed money from an investor to get started.