Is the remaining amount from her father's surgery expenses considered a debt upon her, given that she did not sign any commitment to pay?

Scholars have differed on whether the contract between a patient and a doctor is one of ijarah (definition) (leasing/hiring) or ja'alah (a reward for a specific outcome). However, the preponderant view is that medical treatment is ja'alah. If the contract is ja'alah and stipulates healing, then the doctor is not entitled to a fee if healing does not occur. If, however, the contract is ijarah and the doctor performs the agreed-upon work, he is entitled to the full fee, or a proportionate amount if the patient dies before the completion of the agreed-upon work. In the event that the doctor is entitled to a fee, it must be paid from the deceased's estate before its distribution among the heirs. If the deceased did not leave sufficient funds, the daughter is not obligated to pay the debt unless she was the contracting party or the one who delegated the task.