Is the cost of travel that the father paid for his daughter to search for work in another country considered a debt upon her, especially since she did not find work there, and the father has now passed away?

If a father tells his son that the money given to him is a loan, then the father's word is to be accepted, and the amount is considered a debt owed by the son, to be repaid to the estate after the father's death and distributed among the heirs according to Islamic law. Any heir who is an adult and of sound mind may waive their right to the debt. If there is a dispute as to whether the giving was a gift or a loan, then it is considered a loan.