Theory and Analysis:Soul Divisibility
Soul Divisibility refers to a nature of living beings' souls in Neon Genesis Evangelion allowing them to be split and the resulting fragments thereof contained in separate vessels. These may be the bodies of humans, Angels such as Lilith and Kaworu or Evangelion Units.
The soul's divisible property is observed three in Neon Genesis Evangelion. The first example is that of Lilith's soul divided into the bodies of Rei I, II and III, as well as residing in her own original body. In another instance it is the splitting of Kyoko Zeppelin Soryu's soul during her Contact Experiment with Eva-02 such that the part of her soul which feels maternal love towards her daughter, Asuka Langley Soryu, are held within the Eva Unit's core, causing her to go insane and lose all recognition for Asuka following the experiment.
Lilith
In the case of Lilith, it is unclear as to what extent Rei I, II and III are cloned from her; indeed, the ambiguity concerning Rei's creation itself makes it impossible to tell what exact constituents Lilith provided towards Rei's conception. Even so, it is made clear that Rei's bodies are clones due to her repeated appearance after dying in Episode 21 and Episode 23. In The End of Evangelion Rei III is shown to reunite with Lilith with the words "I'm home" ("tadaima"), instigating the Third Impact; however, the fact that she is cloned from Lilith can be deduced earlier in the series through her distinctive behaviour and unnatural appearance. Throughout the series, Rei acts in a manner seemingly detached from human nature, and constantly has trouble dealing with her own emotions, which she finds unfamiliar and sometimes incomprehensible. Judging by the fact that Rei was created in NERV, and that the only living non-human being in NERV's possession at the time of her appearance was Lilith, the conclusion can be reached that Lilith provided some material for Rei's existence, as well as parts of her soul.
It is also probable that the soul of Rei I, originally from Lilith, inhabits Eva-00. See Eva-00's soul for more details.
Kyoko Zeppelin Soryu
During Soryu's Contact Experiment with Eva-02, part of her soul enters and remains within the core of the Eva Unit, not unlike Yui Ikari's absorption into Eva-01. It is there that the similarity ends, as whereas Ikari's union with the Eva Unit was a complete one both physically and spiritually, Soryu was not fully absorbed and emerged from the experiment physically unharmed. Still, it is clear that the experiment had inflicted a bitter and lasting effect upon her since she became highly unstable mentally, suffering from an inability to recognize her daughter and instead mistaking rag dolls for Asuka. The part of her soul within her was likely deeply traumatized, going through the pain of her husband's infidelity during her illness and she eventually committed suicide, hanging herself along with one of the rag doll “Asuka”s. It is speculated that this part of her soul then reunited with the maternal portion within Eva-02, since her voice begging Asuka to “die with me” is heard alongside her otherwise encouraging words telling Asuka she is still alive.