I always thought it was a misconception to be "half-Jewish". Usually the speaker means one of their parents are Jewish, making them either fully Jewish or fully Gentile.

However, I saw today that the Minchas Chinuch (Kometz HaMincha #347) suggests the possibility of such a status (although in Minchas Chinuch he seems less sure). The case is two people own a non Jewish slave (not an Eved Kenaani, but with קנין הגוף). One frees their half, and the half slave converts. The free half is Jewish, and when the remaining half is freed, it remains Gentile.

I'm looking for other sources which discuss such a status. Maybe they disagree with the concept and say the Jewishness spreads (as Minchas Chinuch suggests, unlike in his Kometz HaMincha). Maybe they discuss the practical ramifications that the Kometz HaMincha brings, or suggest new ones.

I'm already aware the Ben Ish Chai in Benayahu (Eruvin 18a), amongst other places, discusses this concept, and relates it to Siamese twins. The Kometz HaMincha also quotes a Turei Even which discuses this, but I don't know what he says.

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    +1 I was actually going to post this question a couple weeks ago, with this exact case, but I didn't think it was possible; I assumed it wouldn't work, due to the logic you ascribe to the Minchas Chinuch. I'm stunned to see that someone actually suggests that this would work (and more stunned that it's the same person who says it wouldn't). – DonielF Apr 2 '19 at 0:33
  • I seem to have heard of conversions to Judaism "just to be sure", meaning that there is some uncertainty about the person's Jewishness, so the rabbis convert him so the uncertainty is removed. Anybody have a reference on that? – Maurice Mizrahi Apr 2 '19 at 16:00
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    @MauriceMizrahi that's an uncertainty if they're fully Jewish or fully Gentile, so they convert them to resolve the uncertainty. Not related to my question. – robev Apr 2 '19 at 17:09
  • חצי ישראל וחצי גוי באופן שנתגייר חציו - נחלקו האחרונים האם אומרים שפשטה קדושתו ונעשה כולו ישראל (קובץ הערות נו-יח בדרך אפשר), או שנשאר חצי גר וחצי גוי (ופשטה שייך רק במקרה שהחצי הקדוש לא יוכל להתקיים בלי החצי האחר) (קונטרסי שיעורים קידושין יא-ח ד"ה ובמה) files.daf-yomi.com/files/bookfiles/kovets-yesodot-vehakirot/… – ShimonS Feb 21 at 11:36