Does expiation become obligatory for someone who caused an accident that led to the death of his friend three years after the accident?

The perpetrator is responsible for all consequences stemming from the effects of the offense, because these are guaranteed effects of the offense. So, if your friend's illness continued after the accident until his death, you are liable because his death was due to the accident. However, if he recovered his health and then died, you are not liable for anything unless doctors determine that the death was a consequence of the accident.

If the death was due to your error, you are obligated to pay the full blood money (diyah) to your friend's family, along with expiation (kaffara) by fasting for two consecutive months. If the error was shared, then you share in the blood money, and each person is liable for expiation. However, if the accident occurred without any negligence on your part, you are not liable for anything.