No Person held to Service or Labour in one State, under the Laws thereof, escaping into another, shall, in Consequence of any Law or Regulation therein, be discharged from such Service or Labour, But shall be delivered up on Claim of the Party to whom such Service or Labour may be due
The person who escaped such service or labor had to be returned to the party to which the labor or service was due.
That implies more then anything recognizing some sort of legal contract between the party due the labor or service and the person in labor or service to the party.
Legally these would be Apprentices of a guild or a union, indentured servants and debtors working off a debt through service to those that loaned them the money, not slaves. Especially if you believe that slaves were property and no more then cattle or chattel, they could not therefore be considered as persons and would be not be legally bond to a two party contract they could not have entered into any more then a horse or a cow could enter such a contract
The Thirteenth Amendment does not ban any property ownership of slaves, it abolishes the practice of slavery or involuntary servitude except as a punishment for crime where of the party shall have been duly convicted.
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I challenge you to provide a legitimate opposing resource.