What happens during the final scene at the quay?

In the final scene at the quayside, Frank bids Eveline to follow him aboard a ship bound for Buenos Aires. But Eveline chooses not to go with her lover. As with many characters in Joyce's stories, she is caught in the grip of paralysis, unable to forge a meaningful life for herself. Though Eveline has an unhappy home life where she's treated like a maid by an abusive father, her sense of family loyalty as well as her lack of imagination conspire to keep her rooted to the spot, as Frank's plaintive calls melt into the distance. But then, perhaps Eveline never really loved Frank in the first place, and so it would've been a huge risk for her to have traveled all that way with him to Argentina:

He rushed beyond the barrier and called to her to follow. He was shouted at to go on but he still called to her. She set her white face to him, passive, like a helpless animal. Her eyes gave him no sign of love or farewell or recognition.