Antanas Rudkus is Jurgis's father. He is incredibly eager to work, but he is elderly and not very strong. Antanas becomes the first casualty to the family's new American life. He has a great deal of trouble finding a job because there is so much competition for work. But Antanas finally lands a position in the pickling room sweeping up brine. He sees some pretty awful hygiene practices with this brine, by the way. Brine is a preserving agent for pickled meats (and all kinds of pickles, actually). This particular brine has some pretty intense chemicals in it. These chemicals eat through Antanas's shoes and give him sores on his feet that won't heal. Add to that the fact that he has caught a lung disease from all of the drafts in the family house and in his place of business.
Soon, Antanas is in bed coughing up blood. Every morning, he tries to get up and work but he can't because he is too weak. Eventually, Antanas dies. And even though Jurgis and his father have lived together Jurgis's whole life and Jurgis loves the old man, Jurgis cannot afford to give Antanas a real Lithuanian funeral. Antanas's death is another part of Sinclair's message about capitalism, that it is cruelest to the weak and the sick: there is no kind of safety net to give Antanas medical treatment or to make his golden years more secure. (A historical note: Social Security wasn't signed into law until 1934. Critiques like Upton Sinclair's The Jungle made these kinds of social welfare acts possible.)