I don’t know the source of this idea that those [souls among the Nations] who did accept [Torah, while it was offered to all the nations at Sinai — from which only Jews and a few “renegade” souls of non-Jews accepted] are the gerim, but I don’t know what is so hard to understand. The Midrash speaks about [...] indviduals who were renegade souls!I personally know a convert who was adopted by a non-religious Jewish family (while being a non-Jew himself, obviously). When he learned about his status, he decided to convert and took the matter very seriously, studying very hard while going to a particular Jewish school that is not exactly good for infusing life into one’s yiddishkeit, even for a Jew.
On spiritual terms, they are the holy sparks who are ingrained in klippah [spiritual forces of unholiness that shield this world from G-d, making up the material façade of the physical world] and are yearning to get close to kedusheh [holiness].
But, as mentioned in another thread about goyim, the common explanation used by the Rebbe numerous times, which comes from the Chido (but in a footnote in Likutei Sichos, I saw [that] the Rebbe found a source for that concept in some newly published manuscript of Baalei Tosfos) is thus: [Why is it that] Gemara uses the term “ger shnigyir”; apparently the proper term should be “goy shnisgayir”? [Gemara uses such a term] to indicate that the eventual ger has a hidden latent Jewish soul which waits to be discovered and activated.
According the [Alter Rebbe], the geirim are stray sparks which fell in klipeh and are restless until they [become] Jewish.
The [Alter Rebbe] explains that this restlessness has to do with Avraham’s circumcision, which caused that holy souls belong exclusively to Avraham and not to anyone else (until that point, you could have a holy soul and need not convert — as Meshiselech, Mamerei who had great souls, but did not feel an urge to convert), so if a holy spark somehow “fell” into a goy’s body, the holy spark can’t rest calmly in the goy’s body and has an iresistible urge to become Jewish, since Avrahams mileh dictated that all holiness has to be Jewish [by definition].
However, this is only about the offspring of Avraham which were post-mileh, but concerning Yishmoel, since he was born prior to Avrahm’s milah, the [Alter Rebbe] says, we see so few converts from bnei Yishmoel [i.e., Muslims etc.], since they were not influenced by Avraham’s mileh; so if a stray spark enters them, they don’t have the urge to convert.
When it came time for his exam, the judges were astonished by the depth of his knowledge. He became (at least to some degree) a chossid of one of the Chassidic groups. I remember talking to him — when asked why he learned teachings of that particular Rebbe, he answered that they “spoke to him”. Later, a friend of mine saw him amongst Lubavitcher chassidim. This guy told my friend that his chassidishkeit before was fake and superficial, and in attempt to find something real, to which he can hold fast, he joined Lubavitch. If one is seeking emes, one will find it eventually. (This is obviously not a statement about the other Chassidus, to which he belonged before.)