Is someone who fell into a complete coma in Arafat considered to have fulfilled the obligation of Hajj, or is he required to repeat it after recovery?

Fainting after assuming ihram does not affect its validity. If a pilgrim faints after assuming ihram, their Hajj is valid by agreement of the imams.

As for the standing at Arafat, if the fainted person regains consciousness, even for a moment, within the time of standing, it is sufficient by consensus. If they do not regain consciousness until after the standing, then according to the Maliki and Hanbali schools, their Hajj has been missed. The Shafi'i school has two opinions on this. The Hanafi school deems it sufficient for the person to have been present in Arafat after having assumed ihram. Sheikh Ibn Uthaymeen preferred the opinion that their standing is valid because their intellect remains, not having departed. However, it is more cautious to repeat the Hajj if feasible.