In Joyce's short story, "Eveline," Eveline is trapped and figuratively paralyzed in a bad home life. She is the responsible person in her home and takes care of her little brother and her abusive father.
Her going to Buenes Aires is an opportunity to escape. Like other characters in Joyce's short story collection, Dubliners, from which this story comes, she is a Dubliner trapped in Ireland and unable to escape. Moving away to South America would present her with what would most likely be a better life.
But this escape comes at too high a price, apparently. Dubliners features characters that don't get out of Ireland, even when they have a chance. In Eveline's case, she is in a no win situation. To leave would probably present her with a better existence, but would leave her family uncared for. She freezes when it is time to go--she is literally, and figuratively, frozen. She has no good choice. She desperately wants to escape, but cannot bring herself to do so.
It is important to note that this is sophisticated fiction. Eveline does not cheerily stay and idealistically look forward to being the rock of her family or whatever. This story presents no moral lesson. The fiction realistically depicts a woman trapped in a modern situation with no way out. It is dark and honest.