Isma'il narrates from Amir (may Allah have mercy on him) that the children of a mudabbarah (a slave woman to be freed on her master's death) and the children of an umm walad have the same status (as their mothers): when their mothers are freed, their children are also freed, when the master dies.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب عتق أمهات الأولاد / 21801