When Upton Sinclair looked back on his efforts to finish The Jungle later in his life, he remembered that he "went crazy at the end of that book and tried to put in every thing [he] knew about the socialist movement" (source: Ronald Gottesman, "Introduction," The Jungle. New York: Viking Penguin, 1985. xx). The last chapter definitely feels like that: it's chock full of stuff about what keeps the worker down in our current system and how much happier he'll be after the revolution. The relative disorganization in Chapter 31 of The Jungle represents a real artistic problem for Sinclair as he tries to tie off Jurgis's story line while still hinting at a glorious socialist future beyond the final pages of the book.
Up until the last couple of chapters of the book, The Jungle has really emphasized the tragedies of Jurgis Rudkus on his long, slow road to becoming a member of the Socialist Party. In The Jungle's first run as a series of episodes in the socialist magazine Appeal to Reason, it pretty much ended with Jurgis getting arrested at a socialist rally, something that doesn't happen in the novel version. This ending poses a problem, though: Sinclair is truly committed to using fiction to show the value of Socialism in ushering in a new way of life. There has to be some kind of window to a better future. The Jungle is literally a Progressive novel – meaning that it is suggesting the possibility of human progress.
So, poor Jurgis can't just keep getting squashed into the dirt. There is no uplifting message in that. Still, even if Sinclair wants to point to a socialist future he wants his readers to dream of, he also can't get crazy and end the novel with the election of a completely socialist Congress or anything. The Jungle is very clearly set in the here-and-now of the early 1900s. It depicts a barely fictionalized version of the 1904 Chicago Stockyards strike. So Sinclair doesn't want to get into wild science fiction in the last chapter of the book. It has to stay realistic but not be too depressing.
Sinclair walks this tightrope between too hopeful and too grim by ending the novel with a national election in which the Socialist Party has a larger voter turnout than it has ever had before. Jurgis's life has not materially changed – his family is still mostly dead or miserable, and he is a poor man. But Jurgis is now committed to a cause greater than himself, which gives him hope that he has not had since around Chapter 7. The socialist movement becomes Jurgis's life. Even if he isn't doing so great as an individual, he feels great pride in being part of a collective socialist movement that is doing better and better.
This shift from Jurgis as an individual to the larger Socialist Party as a whole is reflected in the action of the novel. The final words of The Jungle come from a Socialist Party speaker at a rally after their relatively successful election. This speaker tells the excited crowd: "Chicago will be ours! CHICAGO WILL BE OURS!" (31.48). There are three important parts to this exclamation. First, "Chicago": Sinclair didn't choose to set his novel there only because the meatpacking plants were disgusting or because there had been massive stockyard strikes in Chicago the year before he started writing. Sinclair also picked Chicago because it really was the home of the American socialist movement at the turn of the twentieth century: the 1904 National Congress of the Socialist Party was held in Chicago (source). Chicago was a real hotbed of union and organized worker activity at the time.
Second, there's the "ours." Who is "we" implied in this sentence? "We" are, of course, the socialists; the socialists are the ones who will have this future Chicago. Not only is Sinclair a dedicated socialist, but The Jungle is first published in a socialist magazine and addressed to comrades of the movement. So, this novel is definitely addressed to a collective, the working people of America. Because one of the whole points of socialism is to put group happiness over individual profit, it makes sense that the focus on Jurgis alone would shift to Chicago socialists as a whole. In other words, it matters that the last words of The Jungle are not Jurgis shouting, "Chicago will be mine!" It's an anonymous speaker saying, "Chicago will be ours!" – all of ours, yours and mine. It will belong equally to the workers of America.
Last but not least, we can't forget "will": "Chicago will be ours!" Sinclair is writing in a fairly realistic mode, so he's not going to end his novel with a perfect socialist paradise. But he does want to use the novel to energize the socialist movement and recruit people to the socialist cause. So he points towards a glorious future that will certainly come, as long as everyone in the movement keeps working hard: Chicago will belong to the ordinary workingman. It's not might or could. It will be ours. Sinclair is sure of it, and he wants us to be sure of it, too.