What is the legal outcome if the slave partially fulfills the Kitaba payments before the master's death, and the Tadbir is activated upon the master's death?

Primary text

If the slave pays part of the contract amount and the master dies, the slave is fully manumitted. If the Tadbir value is within the one-third limit of the estate, the remaining Kitaba obligation is dropped. If the Tadbir exceeds the one-third, the manumission is enacted up to one-third of the estate value based on the Tadbir, the corresponding amount is dropped from the remaining Kitaba obligation, and the slave must pay the residual amount due under the Kitaba.