Purchase of a child from one's parents - Oyamoto Miuke

...However, when the guarantor redeemed her, the ransom money was small and no gift was necessary. This was called "minuke" (or "oyamoto mikuage"), and some customers used this form to avoid losing money. A prostitute who had been bought out was prohibited from returning to work, and sometimes she would submit a "purchase document" to her master (kaenushi) stating that her future livelihood would be guaranteed if the man who bought her left her....

*Some of the terminology that refers to "parental surrender" is listed below.

Source | Heibonsha World Encyclopedia 2nd Edition | Information

…しかし保証人が請け戻す場合は身請金も少なく，祝儀も不要であった。これを身抜け(または親元身請)といい，失費をまぬがれるためにこの形式を用いる客もあった。身請された遊女は再勤を禁じ，もし身請人が離別する際には以後の生活を保証する旨の身請証文を抱主（かかえぬし）に提出することもあった。…

※「親元身請」について言及している用語解説の一部を掲載しています。

出典｜株式会社平凡社世界大百科事典 第２版について | 情報