Someone just told me that a ger earns their Jewish status (on a kabbalistic level) by attaching themselves to a Jewish soul that has gone badly astray and needs to do a tikkun. By offering to do the chesed of helping that straying soul do the tikkun it needs to do, the non-Jewish soul can attach itself to the Jewish soul and join the Jewish people. This is supposed to explain both how a convert can change their status so radically on a spiritual level midlife and why so many gerim seem to have such a rough time of it in life. Has anyone seen a tradition like this inside? My source thinks it might have been the Ben Ish Hai but he heard it orally so he isn't certain.
This concept is explored in the Arizal's Sha'ar HaGilgulim 1:10 (An English translation is available by here)
Some highlights are as follows:
Know, that if a person merits obtaining his Nefesh, Ruach, and Neshama, and then blemishes them through sin, he will have to be reincarnated to rectify the damage...
...When he returns in a gilgul with his Nefesh and he rectifies it, his Ruach will not join him. This is because his Ruach remains blemished, and it cannot rest upon a rectified Nefesh.
The Hebrew word for “convert” is ger, a word that also means “stranger.” Probably both meanings are applicable here. In other words, rectified levels of souls do not reside in the same body with blemished ones. In what was discussed previously, the person was adding non-blemished, new divisions of soul to already rectified divisions of his own soul. However, once he has sinned and must come back another time, the process of tikun changes. He cannot add blemished aspects of soul on top of parts that have already been rectified.
Therefore, his [blemished] Ruach will be reincarnated into another person, joining up with the Nefesh of a convert. The Neshama will likewise do the same.
The Hebrew word for “convert” is ger, a word that also means “stranger.” Probably both meanings are applicable here. The Nefesh that will host this blemished Ruach must be the Nefesh of a convert, but relative to the homeless Ruach it is also the Nefesh of a stranger.
The following section 1:11 explains more of the process.