He remembers Katerina—her charm, her wit, her easy seduction, and her eventual betrayal—and through the centuries after her, that's all he can think about. She was in love with him (foolish human that she was), and he was enamored with her (foolish and blinded vampire that he had been). But he's learned since Katerina, he's grown up a bit—distanced himself from women, doesn't let them get close anymore…not as close as Katerina in any case.
So when he hears the whispers of the return of the doppelganger, he ignores it at first. He wants to stay as far away from Katerina as he can manage—and she's of no use to him now anyway. It's only when there's talk of a second (non-Katerina) doppelganger that he becomes interested.
He takes his time following the hushed whispers to Mystic Falls, a quiet town he remembers from Katerina's past dalliances (yes, he knew of them) and there he discoverers Katerina—except not.
This human girl named Elena Gilbert is kind and brave (maybe foolishly so). She accepts her role and plays it well.
"I'll come with you," she says, her voice not even wavering, "I'll go through with the sacrifice—but you have to promise to leave my friends and family alone."
Klaus tilts his head to the side only slightly and studies her for a moment. For all intents and purposes, she could so easily be Katerina—at least in looks. But he knows Katerina well. She would have gathered an army and put herself firmly behind it. Elena Gilbert, on the other hand, also has an army…but she stands directly in front of it. Klaus then nods wordlessly, holds out his hand, and watches with scrutinizing eyes as this Elena Gilbert puts her hand in his and steps toward him. Neither pays notice to the cries of protest and disbelief from her gathered army.
He spirits her away and she doesn't have to be told she'll never see them again. He watches the tears fall down her face—another difference between her and Katerina, for Katerina never cried for anyone—and resists the urge to wipe them away. He is not her hero in this tale; he is the unmerciful, unapologetic villain.
The tale is not over, however, because Klaus watches the foolish part of himself rear it's ugly head to this Elena Gilbert—she doesn't notice, seems to believe he's drawing out her torture, but in actuality…he's debating with himself. He studies her closely for a while, watching for signs of Katerina; and when he finds none, he's at a loss as to what to do.
He keeps her alive in his large castle far, far away from all that she has known. He watches her adjust to her (what she assumes to be temporary) life. He dresses her up in finery and almost smiles whenever he sees the smudges of dirt on her new clothes or jewels missing in her accessories. She is not a delicate flower, nor does she pretend to be, and he thinks he might love this about her.
It doesn't take him long, only a few weeks, to realize that this human carrying the name Elena Gilbert could be his second chance. He could have someone love him again.
It's when he thinks this life-altering thought that she voices the question that must have been on her mind for months. "Why am I still alive?"
Klaus puts a hand on her cheek, feels the warmth there, and answers honestly for a change. "You're not Katerina, and I don't know how to kill you when you could be so…."
Elena shakes her head. She seems to understand, without him saying the words he hasn't even formed to himself yet, what he desires from her. "I didn't ask for that—I don't want that." Elena backs slowly away from him. "That was not part of what I promised."
Klaus realizes the truth then. She can't be his second chance because he does not deserve one. And this Elena Gilbert could never love him because he is not truly loveable.
He laughs (slightly manically), "You're not what I expected, Elena Gilbert."
She just glares defiantly at him. "I'm sorry I can't say the same—you're everything I expected."
He almost wants to kill her after that remark, but he still finds that he is unable to actually do so. And, in the end, he lets her go. He tells her that the chase is on and that he won't let her go the next time he sees her.
And when their eyes meet, he knows she understands his double meaning.