This is only going to be one part.
During The Titan's Curse, Nico and Bianca di Angelo are brought to Camp Half-Blood. In attempt to escape responsibility, Bianca joins the Hunters of Artemis. She realizes that she still has responsibility and wants to fully escape it, and she finds the perfect chance. The real reason Bianca wants to defeat the robot in the junkyard is because she can use it to fake her death. After the robot collapsed, she crawled out of the junkyard without being seen, and managed to go to camp and tell Nico her plan. This explains why there were no traces of her in the junkyard. When Nico talks to her ghost, she is disguised in order to trick Percy. As a child of Hades, she can most likely appear ghostly. Also when she chooses rebirth, she really leaves to go somewhere where she can be completely free of responsibility forever.
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How Bianca survived The Titan's Curse
FanfictionThis is a theory explaining how ad why Bianca di Angelo faked her death during The Titan's Curse. Theory by me :)