It's hard to break an immigrant, and by "break", I mean make her feel defeated. You can break her heart, for that's universal. But you can't break her soul; she has worked too hard to get to where she is. She endured many transformations and assimilations. She had to make sense of everything in a new way, and as a child immigrant, love was never her concern. Her concern was learning to accept her new self, to love the person she was now free to become. Her concern was to learn to speak up, to break her family's silence, to break limited traditions and find her voice in a country that banned individuality. Those were her concerns, not love.
Once adulthood hit, she then realized "love" was becoming a concern. It was like another battle she had to win. Her heart broke at a later age than her non-immigrant peers and she had a harder time accepting that people could be deceitful, that they could lie, hurt, cheat, and abandon her. She despised, dreaded the feeling of abandonment. It was rooted deep within her as a child, and grew as more people left the country that was once a homeland. Abandonment is a common event in an immigrant's life.
She goes for runs across the bridge. On the island, she is surrounded on both sides by water, and the beautiful sights that make New York what it is remind her that she can not break. She must keep going. A heart can eventually heal; people come into one's life, not necessarily to stay, but to inspire, or make one realize something they hadn't known before. People, she learned, were not always permanent. And as much as that truth hurt in its own way, she decided to cope with it and remain strong, and when she ran she felt the strongest. Unlike the permanent tattoo below her heart that contains the names of loved ones she never met, most things are impermanent. Some are worth fighting for to keep, others are best abandoned.
Yes, abandonment was now a word she accepted.