The slave is considered chattel - property - to be bought and
sold in perpetuity like livestock. Once an individual becomes a
chattel slave they are considered chattel for life. Not all forms
of forced labor doom a person to slavery until the day they die.
Many of them are only for a fixed period of time or until a fixed
debt has been redeemed.
Children born to chattel slaves are considered the property of
the "owner" of the chattel slave just like a calf is the property
of the owner of the cow. No other form of forced labor passes that
status/lifetime-obligation down to the children.