Time (2006) on Netflix

Seh-hee and Ji-woo have dated for two years; jealousy consumes her. She worries he will tire of her face. Then, she disappears. Telling no one, she goes to a plastic surgeon for a new face. Ji-woo has no idea where she is, although when he does respond to other women, someone unseen intervenes. Then, he meets See-hee, and although he tells her he misses Seh-hee, this new relationship blossoms into love. They talk at the same coffee house, visit the same sculpture park, and pose for the same photographs he did with Seh-hee. We know they are the same woman. Has this new face and renewed love made her happy? And what will Ji-woo do when he learns the truth? Is losing face losing self?