You wouldn't really have slaveholding in a free society, because slaveholding implies a violent act of coercion. A slave is stripped of their rights and so are all of their descendants, thus it's implied that they aren't really free to make their own decisions and you've used violent coercion to obtain them in the first place. Slaves can't exist in a free society.
What you would likely have is two forms of servitude which would be the closest thing to a "slave" in an Anarchist society.
1) Contracted Servitude
Contracted servitude would be a matter in which your rights have not been violated, but you've agreed to set conditions that could in fact be considered "slavery." Pretty much under contracted servitude, you voluntarily give away some of your rights to another in exchange for something. That something could be food, shelter, money, experience in a trade, or any combination of the above among other things. In exchange, you agree to give your owner a monopoly over your labor for a set period of time (whether that labor is sexual, manual, intellectual, or some combination of the above). Your children are not held to that contract nor can you make your children part of said contract except in the form of adoption. Effectively you are still a free man, you're just an "apprentice" or "indentured servant" working for an individual. If that individual violates that arrangement (such as via sexual harassment/assault) you could terminate your contract at any point and the courts would uphold your decision based on an anarchist version of common law.
2) "Reparations Servitude"
If you don't own the property to sell off, and you're too lazy to actually work off your debts via payments agreed to in an arbitration/court hearing, a case could be made to voluntarily put yourself into a form of servitude to cover reparation expenses for a crime or foul that has been committed against another. This would assume that both parties consented to this form of reparations, and like in the first example, you would still have basic rights that would make you a servant, not a slave.
Could the definition between servant and slave be very thin based on the sort of contract? Probably. The major thing is that if your "owner" was causing you mental or bodily harm, you'd have a case against them in a private court of law under servitude, whereas you would have no such rights under slavery.