Cat Loss Syndrome

Since the death of his cat, Nabi, Seungwon has struggled to get his life back on track. One day, he finds himself wandering the streets with no particular destination.
A Woman in the Rain
He notices a woman standing in the exact spot where he first found Nabi. The encounter takes an even stranger turn when he sees how she behaves.
Something Familiar
Her mannerisms remind him of his cat, making an ordinary stranger seem oddly familiar.
Who is this woman, and why does she remind Seungwon so much of Nabi?