Salvaging
Salvaging is the act of extracting a soul from a donor and embedding it into a clone or one of the Evangelions. The donor my be alive, as in the case of Yui Ikari (Eva-01) and Kyoko Zeppelin Soryu (Eva-02), or deceased as in the case of Rei I, parts of whose soul where transfered into Rei II and Eva-00, Rei II, whose Soul was transfered into Rei III, and Kaworu Nagisa , possessor of Adam's soul, whose soul was transfered back into the Adam embryo (in Gendo's hand), after his death.
Salvaging was also attempted on two occasions in order to fix a soul into a re-creation of its original body. These attempts were both failures, although Shinji did re-form on his own shortly after the attempt to salvage him failed. The earlier attempt to salvage Yui's soul failed completely, and she remained in Eva-01. However, this attempt did somehow result in the creation of Rei, a person based upon Yui's DNA who possessed Lilith's soul.
The exact mechanics of soul salvaging are never detailed, but when the donor is living, it involves a Contact Experiment.