I think this is what they're referring to, the biblical "split the baby" proposal (from Wikipedia, see link below):
"The story is recounted in 1Kings 3:16-28. Two young women who lived in the same house and who both had an infant son came to Solomon for a judgement. One of the women claimed that the other, after accidentally smothering her own son while sleeping, had exchanged the two children to make it appear that the living child was hers. The other woman denied this and so both women claimed to be the mother of the living son and said that the dead boy belonged to the other.
After some deliberation, King Solomon called for a sword to be brought before him. He declared that there was only one fair solution: the live son must be split in two, each woman receiving half of the child. The liar, in her bitter jealousy, exclaimed, "It shall be neither mine nor yours—divide it!" However, upon hearing this terrible verdict, the boy's true mother cried out, "Oh Lord, give the baby to her, just don't kill him!" The king gave the baby to the real mother. King Solomon's judgement heard throughout all of Israel and thought to be wise."
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It's a biblical reference, not a legal term. There is no legal significance to the term.
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