פירוש על קידושין 34:13

The Torah says that the slave who has his ear bored shall serve the master forever—he serves the master but if the master dies he goes free. He does not serve the master’s children.

Leviticus 25:50 refers to a Jew sold to a non-Jew. When being redeemed the Torah refers to a negotiation with the Jew’s purchaser. From here we can conclude that only the purchaser can own the slave, and not one of his children. The slave goes free if his/her master dies.