Is there a point that standing up against a bully stops being self-defense?

For instance in the case of the girl that smashed the female bully's head against the pavement more than once and left her with brain damages, thats not self-defense anymore.

Or let's say a bullied victim has enough and punches his bully. The other guy started bleeding but the victims continues delivering blows and won't stop even when he's on the ground, badly injured. At that point isn't it aggravated assault?

Is there a point that standing up against a bully stops being self-defense?
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