One common theme is friendship. Gaara and Sakura, who come from different villages, form a bond through the act of saving. It shows that even characters with different backgrounds can be friends.
In many Sasuke - Sakura - Gaara fanfictions, Sasuke saving Sakura from Gaara can be a really exciting plot. It often shows Sasuke's strength and his hidden feelings for Sakura. Maybe he uses his Sharingan to outwit Gaara's sand attacks and rescue Sakura just in time.
Well, in many such fanfictions, Gaara might use his sand powers. He could sense Naruto is in danger through his connection to the sand or his own instincts. Then, he'd quickly move in, using his sand to shield Naruto from any attacks by the Akatsuki members, like blocking their jutsu with his powerful sand barriers.
One popular 'gaara saves sakura fanfiction' might be 'The Desert's Rescue'. In this story, Gaara uses his sand powers to shield Sakura from a powerful enemy attack just in time. It shows his quick reflexes and his growing bond with Sakura.
One great example could be a fanfiction where Naruto has to battle a powerful new enemy who has kidnapped Gaara. Naruto uses his new jutsu and his unwavering friendship to break through the enemy's defenses and save Gaara. Another might be a story set in an alternate universe where the circumstances of Gaara's capture are different, but Naruto still goes to great lengths, even sacrificing his own safety, to rescue Gaara.
Their relationship would likely deepen with trust. Naruto would be extremely grateful to Gaara for saving him, and this would strengthen their bond. They might start sharing more about their past traumas and how they overcame them.
A common plot point is danger. Fem Gaara is often in some sort of life - threatening situation, like being attacked by enemies. Naruto then uses his skills, such as his Rasengan or his ability to make friends out of foes, to save her.
Well, a plot point that often appears is that Naruto is in a fight where he is clearly outmatched. Gaara steps in not just to save Naruto physically but also to save his spirit. Maybe Naruto is starting to doubt himself, and Gaara's timely arrival and words of encouragement along with the rescue remind Naruto of his own strength. And sometimes, the fanfiction might explore how this event changes the relationship dynamics between the two villages that Gaara and Naruto represent.