Perhaps Naruto breaks Hinata's heart by not believing in her. Hinata has always been there for Naruto, but if Naruto starts to doubt her loyalty or intentions, it could be a huge blow to Hinata. For instance, if there is some false rumor about Hinata and Naruto believes it without giving her a chance to explain. This lack of trust can be extremely painful for Hinata and break her heart.
In some fanfictions, Naruto could break Hinata's heart by choosing another girl over her. For example, if he decides to be with Sakura instead. Hinata has always had deep feelings for Naruto, and seeing him with someone else would shatter her heart. It could also be that Naruto ignores Hinata's sacrifices for him and takes her for granted, which slowly breaks her heart as she realizes he doesn't value her as much as she thought.
One consequence could be that Hinata tries to move on but struggles a great deal. She might have a hard time opening up to anyone else in the future. Her self - confidence could also take a big hit. Since she put so much of herself into her feelings for Naruto, having her heart broken could make her question her own worth. Maybe she starts to think that if Naruto didn't love her, then no one will. This could lead to her being more reserved and less likely to take risks in relationships or in other aspects of her life.
He might become really withdrawn. Naruto is a very emotional person, so if Hinata breaks his heart, he could isolate himself from his friends and the village. He would probably be too hurt to face them.
At first, Naruto would be in denial. He has always seen Hinata as someone who supported him. But as the reality sinks in, he would be heartbroken. He might try to find ways to win her back, showing her how much he truly cares. He'd also be very sad and might even lose some of his usual cheerfulness for a long time.
Maybe it's a jealous rival of Naruto who wants Hinata for himself. He manipulates situations in such a way that Hinata ends up hurting Naruto. For example, he could stage events to make Hinata think Naruto has betrayed her trust.
Well, it could be that Hinata starts to ignore Naruto for some reason, like she falls in love with someone else. Maybe she gets influenced by some external force or false information that makes her believe Naruto isn't good for her. This sudden change in her behavior towards Naruto would break his heart as he might have deep feelings for her.
Well, it could be that Hinata might break Naruto's heart by choosing someone else over him. Maybe she realizes she has feelings for another character, like Sasuke perhaps. This would be a huge shock to Naruto as he has always seen Hinata as a special person in his life.
It could be that Hinata publicly humiliates Naruto. She might expose some of his deepest insecurities in front of the whole village. Since Naruto has always been striving for the village's acceptance, this betrayal from Hinata, who he loves, would be a huge blow to his heart.
Naruto could be initially in shock. Given his strong feelings for Hinata, he might not believe it at first. He could try to talk to her and ask for reasons, hoping to fix things.
Hinata may become more assertive. Since she has Naruto as her 'weapon', she has to take on a more leading role. She might have to make decisions about when and how to use Naruto's powers, which could make her grow in confidence.
In many fanfictions, Hinata's confidence grows. For example, she might start taking on more leadership roles in missions with Naruto. Since she has always been shy, in fanfiction, she could break out of her shell more, especially when Naruto is in danger. She becomes more assertive in protecting him and their relationship.