Julian, grasping the head of the weapon, attempted to draw it forth, but in vain – the sharp steel cut his fingers, and the pain and loss of blood caused him to fall fainting from his steed.
1 Answer
Fainting tells us more about how and why Julian falls from his horse. So it is a participle used as an adverb modifying caused him to fall.
It's a construction that English speakers use all the time:
The dog came panting into the house
The girl ran yelling out of the room.
The hounds streaked baying after the fox.
https://www.usingenglish.com/forum/threads/119710-participle-as-adverb