Is expiation (kaffarah) obligatory for someone who died in a car accident with another person, and the one who caused it is unknown, or for someone who unintentionally caused a car accident leading to the death of another person? And what is the method of performing the expiation if it becomes obligatory, and is it permissible to distribute it among the heirs, or to pay money for someone to fast on their behalf?

First: Expiation and blood money are obligatory if the driver was negligent, and nothing is binding on your father unless a judicial ruling is issued obligating him to pay blood money.

Second: If the traffic authority determined that 75% of the fault lies with your brother, then he is liable for the expiation for accidental killing, which is freeing a slave. If a slave is not available, then it is fasting for two consecutive months. Since your brother passed away, if a believing slave is found, their value should be taken from his estate to free them. If a slave is not found, you are not obligated to fast on his behalf, but it is recommended for one of his relatives to fast on his behalf, and one person must fast for the two consecutive months. If you cannot find anyone to fast except for a fee, there is no harm in that.