Throughout Elfen Lied, we have seen many characters who, under the horrific circumstances of the world they live in, eventually broke, sometimes even succumbed to the darkness.
Nana is, however, as close she was to that abyss, one of the most notable exceptions in the whole of both versions of the story.
She is perhaps the strangest case of a character archetype in this tale: The Pollyanna. An unfailing optimist, Nana is a girl with an unbreakable hope that things will get better.
Such an outlook, for the most part in the series, is brutally deconstructed and destroyed multiple times. Lucy's desire for love and companionship is met with betrayal and deceit, breaking her mind to the point her hopes for a happy conclusion end up dashed by her mistakes, for which she's ultimately unable to atone for in life completely. Kurama's decision to do what he saw as necessary brings him to ruin as he finds that his human heart is hypocritically unable to terminate his daughter. Yuka's dream of a fairytale reunion with Kouta is ground to dust when she finds her dream boy had become a shell of his former self. The list goes on.
When Nana is first introduced, she had already spent seven years locked up in the Diclonius Research Institute, subjected to inhuman conditions and treated as little more than a test subject for brutal experiments. Yet, unlike so many sharing her fate, she does not break under the pressure. She managed to find a rock, a foundation to hold onto to retain her sanity.
That rock was Kurama, her "Papa". That man was the only person in that nightmarish facility that treated her with any semblance of kindness. As a result of that, Nana developed a strong emotional dependence on him, this bond helping her endure the harsh conditions of her life up to that point. This also made Nana a very docile and loyal person, willing to do anything for him.
This loyalty will come to the first real test when Kurama came to her cell to give her a grim order: Kill Lucy.
Despite her deep loyalty, she steadfastly refused, valuing the ideals Kurama instilled on her over obeying a direct order. In turn, this seems to have made him rethink his goal, and instead opted to tell her to simply locate her and secure her for capture.
With that as her new directive, Nana was fielded into the city to confront Lucy. After finding her, she contacted Kurama and, decided to impress him, set out to face her on her own, and a brutal psychic duel ensued. However, her enthusiasm for pleasing Kurama, coupled by both her own inexperience and docile nature, caused her to waver in a critical moment, which the ruthless Lucy capitalized by savagely ripping her limbs off.
After the horrific experience, Nana was evacuated and kept hidden by Kurama, fearing repercussions from Kakuzawa. The Chief, however, ordered him to dispose of Nana as soon as possible, leaving Kurama with limited options. In the meantime, she was outfitted with prosthetic limbs, and slowly learned how to manipulate them with her vectors, never once losing her optimism, even after such horrific trauma.
Unfortunately, the ruse was soon found, and, under pressure from Kakuzawa, Kurama was forced to pretend to euthanize Nana, who Kakuzawa now saw as useless. Kurama acted quickly, pretending to administer a lethal injection to Nana, which instead contained a powerful sedative to put the girl to sleep. Nana, however, seems to have been aware to a degree of what Kurama pretended to do and, as he proceeded it, gave him a tearful goodbye before losing consciousness.
The next time Nana opened her eyes, she was alone in the beach, having been shipped away into the shores of Kamakura, with nothing more than her dress, a note (or recording, depending on the version), and a purse full of money.
Alone in a land she did not truly know, Nana was barely able to process her new situation before being attacked by Bando, who had mistakenly assumed she might have known Lucy's location. The argument escalated, and Bando viciously attacked her both physically and psychologically. The result of the realization of her newfound loneliness, added to Bando's casual cruelty, lead to a crack in Nana's optimism, and, perhaps for the first time, awoke the darkness she didn't even knew she had within.
In a seeming trance, perhaps controlled by a dark influence, Nana stood up, stating that at Bando's cold words of her being unwanted to the world, she would reply by carving a place for herself, killing all who opposed her.
A fight between the two ensued, and while Nana quickly gained the advantage and cornered him, a surprise attack from Bando helped to snap Nana back to her senses.