Existential confusion
Either Caroline's father kidnapped her from her mother and stepfather, or else, Caroline's 'father' is not her father at all, but just a random kidnapper. There is not way for Caroline to know the truth, and when she reaches her childhood home to investigate her feelings there, she finds no connection to the family she knew as a small child. This father-less-ness, along with Caroline's homelessness, indicates an existential dilemma. Because Caroline doesn't know who her real family is, she doesn't know who she is, and since she has no home and no community, she must invent a life for herself by finding a job, trying her life at the real world.
Coming of age
In many ways, My Abandonment is a coming of age story, a Bildungsroman, because the hero is on the cusp of her adulthood, and the drama of the novel deals primarily with Caroline's dilemma between her peaceful, reclusive life with her kidnapper, or the difficult, confusing world of regular people. When she chooses to get her high school diploma and find a job, she has successfully entered the adult stage of her life.
Paranoia and trust
Caroline doesn't know whether to trust her 'father,' partly because their story suggests that she was kidnapped, but also because he is extremely paranoid. She learns about his paranoia, and although she doesn't share his traumatic history, she does understand what it feels like to be detained, and to be under someone else's control (like CPS). Later, Caroline watches her long lost sister from afar. She wonders about whether she should have trusted her father all those years ago, showing that she has trust issues and paranoia of her own. Eventually, the paranoia drives her away from community, and what's worse: she looks for a new little girl to abduct.
