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While Ichigo Kurosaki underwent training to gain his own Shinigami powers, Kisuke Urahara puts Ichigo's soul through a process called Encroachment, where if Ichigo does not gain Shinigami powers on his own, he will become a Hollow. Tessai Tsukabishi severs Ichigo's Chain of Fate.
So far, no. She was last seen in the manga healing Ichigo's wounds inside of the Garganta so he could fight Aizen. I doubt she'll die very easily though. After all, in the arc where Urahara and Tessai escape from the Soul Society, Captain Kyoraku and Captain Ukitake kept on saying how frightening Captain Unohana is. If she can scare students of Head Captain Yamamoto, I think she can hold her own in a fight.