Jin loved his wife. There was no question of this. But he'd meant it when he'd asked Locke not to bring her back, and he was fully prepared to give up life with Sun in exchange for her safety. He accepted his fate with the resignation of a man who has known far too much disappointment.
He still dreamed about her during his first few weeks with the Dharma Initiative. The day on the beach when they had been helping Claire catch birds was one of these, and he always woke up afterwards thinking why that dream? That day had been no better than others; in fact for he and Sun, it was hardly romantic.
Gradually the dream shifted, and six weeks in, he'd caught a bird for Claire and brought it to her so she could attach the note to it. She'd rewarded him with a broad smile and a kiss on the cheek. Then she'd grasped his hand in hers and they'd released the bird and together watched it fly away. Sun was nowhere to be seen.
He chalked it up to fantasies of escaping the island and threw himself into the search that Sawyer—LaFleur—had ordered. The dreams didn't end. If anything, they only got worse until they no longer even resembled a memory. Now he and Claire were walking on the beach together, holding hands and talking. Language was no barrier, and he told her of his impoverished childhood, his enlistment in the army, and his string of disappointing jobs. She reciprocated with tales of her absent father, comatose mother, and Goth phase. He laughed trying to picture this sunny, cheerful woman with black hair and clothing and listening to bands with skulls on their album covers.
"I love our walks," she tells him. "Not that I don't love Aaron, but sometimes I just need a break, and this…"
He kisses her before she can finish, and she feels so small in his arms, like he could break her if he squeezed to hard, but he knows that she's stronger than he could ever imagine.
She kisses back and her fingers go to the buttons on his shirt. He tries to still them—he wants to be a gentleman, because that's what she deserves, but she whispers, "I think we've been dancing around this long enough," and continues.
Afterwards, when they're lying in the sand and he's stroking her hair, she says, "Why aren't you searching for me, Jin?"
That's always when he wakes up.