As mentioned in this answer according to the Arizal, one of the reasons for the daily blessing of not being made a heathen is that
each night a person returns his soul to the creator and it[sic] possible that this soul be switched into another body or state of being. ...each day ... a person awakes to find himself in this particular configuration of body and soul
Source: eitz chayim, heichal adam kadmon, shaar alef, anaf heh. CF Likutei Halachos (R' Nathan Sternhartz) Yoreh Deah, Basar B'Chalav 4:1
The implication being that there is a possibility that a Jewish person could have his/her soul incarnate into a non-Jew.
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