Maybe Kakashi. He's been Naruto's teacher and mentor. He has the skills and the loyalty to Naruto. He could use his Lightning Blade technique to quickly reach Naruto during the fall and carry him to safety.
He could get seriously injured. The Hokage monument is very tall, and the fall would be a long one. Naruto might break his bones or worse.
One possible plot could be that Naruto is facing extreme self - doubt. Maybe he feels he has failed the village in some way, like not being able to prevent a major disaster. So, in a moment of despair, he jumps off Hokage Mountain. But then, his friends sense something is wrong and come to his rescue just in time. They then have heart - to - heart talks with him and help him regain his confidence.
Sakura would be extremely distraught. She has always cared deeply for Naruto, and seeing him in such a dangerous situation would make her rush to his aid immediately. She might use her medical ninjutsu to heal him if he's injured. Kakashi, on the other hand, would be shocked but also proud that Naruto has the courage to face his inner demons in such a drastic way. He would try to understand Naruto's motives and help him get back on track.
The village's morale could take a huge hit. Naruto is a symbol of hope and strength. If he jumps off the monument, it would make the villagers question their own safety and the stability of the village. Politically, it could cause unrest as the village leaders would have to deal with the aftermath and try to keep the situation under control.
In some fanfiction scenarios, Naruto might jump off the Hokage monument to follow someone or something. For example, if there is a mysterious figure or a spiritual entity that he believes he needs to follow, and the only way seems to be by jumping. It could also be a symbolic act of breaking free from the expectations that come with being associated with the Hokage monument.
Sasuke could be the one to save Naruto. Despite their past differences, Sasuke still has a connection to Naruto. He might sense Naruto's danger and rush to his aid, using his Sharingan to find a way to safely get Naruto back up from the bottom of the cliff.
On the positive side, it could boost his reputation among some of the younger ninja. They might see him as a fearless and rebellious figure. However, it could also create a divide in the village. Some would admire his boldness while others would condemn his actions as reckless and irresponsible.
Perhaps Naruto jumps off the Hokage heads as part of a training exercise in the fanfiction. He might be testing his new skills, like a new form of chakra control or a new jutsu that allows him to land safely. It could also be a bet with his friends, like Sasuke or Sakura, to prove his courage and abilities.
It could be the First Hokage, Hashirama. Naruto would be amazed by his powerful Wood - Style jutsu and his ability to create the village. He could learn about the original ideals behind the Hidden Leaf from Hashirama.
Sasuke could save him. Despite their differences, Sasuke might still have that underlying bond with Naruto and show up just in time to catch him or pull him to safety.