I disagree with how you guys are interpreting this. Aine's contract isn't for Nagi's benefit, it's for Aine's. By the contract, if any part of the property is damaged, the contract is broken and Nagi is thrown out. Aine is included among the property. What counts as damaged? Physically hurt? Emotionally hurt? What if she's just sad or unhappy living with him? That sadness could be interpreted as damaged and the contract will be revoked. As such, while Aine's responsibility is to take care of the property, it is Nagi's responsibility to take care of Aine such that she is always satisfied, else she always has the option to quit and take away the property from Nagi.
Letica might like Nagi for his help, but she did this for Aine, not for Nagi. I get Aine can be considered a slave because she becomes tied to the property and Nagi gains all of the property, but it honestly sounds like she's just a maid by how the Aine-Letica contract was worded. I believe the slave part is more for the sake of forcing Nagi to be her caretaker than for Nagi to actually own her.