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1.
The mother of Sephiroth and Hojo's lover and in some cases wife. Her full name is Lucrecia Crescent.

Originally she worked as a partner for Grimoire Valentine, but ran away after feeling she was to blame for his death. After this event she also shunned Vincent, his son who fell in love with Lucrecia.

Lucrecia was asked to do a job in Nibelheim, which she took finding it as a way out of the guilt and having to face Vincent. This was not to be, after he took a job as a bodyguard to protect the sicentist, including her.

Eventually after Vincent confessed his love, Lucrecia couldn't bare it. She pulled away and ran to the warm embrace of Hojo, who she stayed with.

She later became pregnant with Hojo's child and was one of the first people to be injected with JENOVA cells. After suffering many faints and collapses she gave birth to Sephiroth, only she never got to hold her child once.

She later disappeared, only to be found again later in the game in the secret waterfall area. After being told by Vincent that Sephiroth is dead she seals herself in a giant Mako Crystal, due to sorrow and the fact she cannot die because of the JENOVA cells.

In Dirge of Cerberus, Lucrecia is seen as the saver of Vincent, experimenting on him and making his body less human by inducing Mako into it and Chaos.
Vincent: ...... Lucrecia. The woman who gave birth to Sephiroth.

Cloud: ...gave birth...? Wasn't Jenova Sephiroth's mother?

Vincent: That isn't completely wrong, but just a theory. He was born from a
beautiful lady. That lady was Lucrecia. She was an assistant to Professor Gast
of the Jenova Project. Beautiful Lucrecia.

Lucrecia: I wanted to disappear... I couldn't be with anyone... I wanted to
die... But the Jenova inside me wouldn't let me die... Lately, I dream a lot of
Sephiroth... My dear, dear child. Ever since he was born I never got to hold
him, even once... Not even once. You can't call me his mother... That... is my
sin...
by Queen Yam October 13, 2006