Well, I don't honestly think Hassan needs to be reconciled with Assef. Let us remember that before, when Hassan threatened Assef with his slingshot and said that he would be known as "One-Eyed Assef" it was because he was threatening his master, Amir. Hassan stood up to Assef and showed considerable bravery in the way in which he did this. Assef clearly shows himself to be a bully who is in love with violence, and therefore I don't think there is any sense in which Hassan needs to be reconciled to Assef at all.
Let us remember that the chapter you have indicated in your question. Chapter Seven, is when Assef finally gets a chance to have his revenge on Hassan. Having finally got him by himself without his slingshot, Assef is able to do what he wants to him out of revenge for shaming him before. Consider the following quote:
"Where is your slingshot, Hazara?" Assef said, turning the brass knuckles in his hand. "What was it you said? 'They'll have to call you One-Eyed Assef.' That's right. One-Eyed Assef. That was clever. Really clever. Then again, it's easy to be clever when you're holding a loaded weapon."
Assef is out for revenge, and now that he has his enemy defenceless, he is able to do what he wants to him. This is of course the event that defines the entire novel, as it leaves Amir full of guilt. If any character needs to become reconciled after this event, it is not Hassan, but Amir, after watching his friend suffer so greatly and doing nothing to help him.