This is the reason why Abaye was an orphan who never saw his mother or father, (Kidushin 31b) hinted to in the verse, "Asher bicha yerucham yatom/for it is with You that an orphan finds mercy" (Hosea 14:4) - the head-letters spell ABYY/Abaye. This is because his nefesh, ruach, and neshama are from Cain, the entire root of which is the level of nefesh only. Since he is from malchut, (which is) the level of nefesh, in the secret of nefesh Adam.1 Therefore he is called orphan, since he is only from the level of nefesh which is called orphan.

As mentioned, the Tohu lights departed and ascended above. This creates a quality of separateness in those who are from it. One of the ways this comes out is through being an orphan.

In many places, the Torah groups the Levite, the gair, the orphan, and the widow together. (Deut. 14:29 & 26:12) Above, the concept of the gair was explained, how he leaves family ties etc. The orphan is similar in that he is devoid of family connection. The Levite has no portion in the land. A widow also is left without primary family relationship.

...children’s primary conceptual springboard to relate to G‑d.

The Maharal explains that parents are children’s primary conceptual springboard to relate to G‑d. One who has no parents lacks an intermediary and as of necessity ends up having a more direct connection. Abaya’s intense Cain root afforded him intense direct connection to the One above.

"The supernal family." (Zohar) The soul levels are also as a family to each other. Nefesh, the lowest level, looks to the ones on top for support and guidance.

A lack creates desire and a need to be fulfilled. (Likutei Moharan) One who comes from nefesh alone is as a spiritual orphan. Again, this may be set up by Providence to spur him on to achieve special direct attachment to G‑d.

This is similar to what it says in Sefer HaTikunim, (Tikun 11) regarding the matter of repayment from the property of orphans: "When the neshama is removed, what remains behind is the nefesh and ruach of orphans, etc." Since Abaye was an orphan, because all of his sections were from Cain, he was able to produce souls for converts without separation from his wife, because they too [having left their family] are like orphans without a mother and a father, as the law says. (Choshen Mishpat)

This is the matter: All mixtures of Cain with the rest of the soul-sparks that happen without the involvement of a mother or father are called orphans. Thus converts are called orphans, since they lack a Jewish mother and father at the time their souls are born.

[Translation and commentary by Perets Auerbach.]