She was programmed to terminate anyone she deems as hostile subjects that came near the Gate. Nu-13 is also shown to have a split personality, split between an emotionless girl when around others, and a yandere when around Ragna the Bloodedge, though this may be how she was programmed to act. Nu-13 wants to absorb Ragna and have him join her in destroying the world, because she, too, possesses a piece of the Azure Grimoire (although neither she nor Ragna realized the pieces they possess were actually imitations). When Ragna refuses to join her, she decides to take him by force. She also knows Hakumen, recognizing him as a "Sankishin Unit".
She, as with Noel, was made as a replica of Saya, Ragna and Jin's sister. They seem to share some of Saya's memories, though nothing congruous. In the true ending, she tries to merge with Ragna by falling with him into the Cauldron. However, Noel thwarted her efforts and saved Ragna's life. Nu dies after falling back into the Cauldron and failing to fuse with Ragna.
In BlazBlue: Continuum Shift, she is replaced by Lambda-11 of Sector Seven. However, she returns as Lambda's Unlimited form in the console versions. She, in Lambda's body, assists Tager on Kokonoe's orders, though her memories are suppressed. Eventually Hazama coaxes her memories as Nu, causing complications in her programming. Under Phantom's influence, Lambda is forced into a battle against an illusion of Nu in her Story mode, becoming comatose if she loses.
In the True Ending of the story mode, Nu arrives just as Hazama is about to deal the final blow to Ragna. Her memories having fully returned, Nu takes the blow herself to protect him. She collapses into Ragna's arms, saying that she dreamt of him while she was in the Boundary, and that she'll always be with him, her body disintegrating. In the process, she gives Ragna her Idea Engine, which allows him to bypass Hazama's negation of the BlazBlue, making even Hazama nervous. After the credits, Relius and Hazama can be seen looking into a cauldron saying "It's amazing how she can regenerate just by will!", hinting that Nu is still alive.
[Source BlazBlue Wiki]
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