Is it obligatory to make up or offer expiation for someone who had a tooth extracted in Ramadan and bled for four days, with the possibility of swallowing the blood during sleep?

Extracting teeth does not break the fast during Ramadan, unless the fasting person intentionally swallows blood. If he swallows it unintentionally, it does not affect his fast. Therefore, there is no need to make up for the days when blood came out, nor is expiation required.