Can Hadd punishments be given to slaves by the owner, without the ruler's permission?

Al-Shawkaani said: It was narrated from Abu’l-Zinaad from his father that the fuqaha’ of the people of Madeenah used to say that no one should carry out any of the hadd punishments except the ruler, **unless** it is a man carrying out the hadd punishment for zina on his male or female slave. Nayl al-Awtaar, 7/295, 296. https://islamqa.info/en/answers/8980/who-is-the-one-who-should-carry-out-the-hadd-punishment-for-zina Usually if one did zina, the case is analysed and witnesses will be assessed by the state to give hudud. But is it the same when it comes to a slave doing zina? The quote above seems to imply that the state is not involved in giving the hudud punishments on the slave and it is only the owner who decides. What if the owner is unjust?