Ata' bin Abi Rabah (may Allah have mercy on him) says: If he made a kitabah contract while he had no children, then children were born to him from a slave woman, and the father died, the price will not be reduced for them; they will remain on their father's kitabah, and if they wish, the kitabah may be cancelled and they remain slaves.
Hence we say: When a mukatab or a mukatabah dies without paying the amount, they remain slaves, and their children will also be slaves, with the evidence being the hadith: "If even one dirham remains due from him, he is still a slave."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب المكاتب / 21704