Before looking at how James Joyce depicts Dubliners in his short story "Eveline," it helps to look at how he envisions the inhabitants of Dublin in his short story collection (Dubliners) as a whole. For the most part, Joyce sees Dubliners as "paralyzed" individuals. This does not mean that they are actually physically unable to move; rather, Dubliners are paralyzed because they are unable to grow, progress, or move forward in a meaningful way (at least, according to Joyce's interpretation). Thus, many of Joyce's main characters are stuck in a largely unfulfilled existence. Most characters realize this fact through climactic epiphanies, one of Joyce's most famous literary tools.
Now, let's look at "Eveline" within this context. The eponymous character of the short story is a young woman who leads an abysmal existence. Her mother is dead, and so she is forced to work a dead-end job to make ends meet and to help care for her younger siblings. To make matters worse, Eveline's father is an alcoholic who drinks up much of her earnings and verbally abuses her. Eveline spends much of the story looking out a window onto the street (an image which exemplifies exactly how trapped she is) and ruminating on her sad existence. However, when she is given the opportunity to run away with a man and leave behind the confines of her life, Eveline chooses to stay home.
It's clear, then, that Joyce's portrait of Dubliners in "Eveline" is consistent with his depiction of the city dwellers in the rest of his short stories. Like her urban compatriots, Eveline is stuck in a dead-end world that has little hope of progressing. Thus, in "Eveline" and elsewhere in Dubliners, the inhabitants of Dublin are metaphorically paralyzed. By depicting Dubliners in such a way, Joyce highlights the oppressive experience of living in Dublin at the beginning of the Twentieth Century.