You're My Pet (2011) on Netflix

Plot summary

On a rainy night, Ji Eun-yi finds a large blue box in front of her home with a young man, Kang In-ho, sitting inside it. Her fiancé has left her for his mistress, and she has been demoted at work. She brings the soaking wet stranger into her apartment and tries to reach her younger brother by phone, but he does not answer. In-ho reminds her of Momo, the dog she had as a child, so she proposes an arrangement: he may stay with her if he lives as her pet dog named Momo. He agrees, and she gives him room and board.