Of course, just because a romance is strange does not mean it is inherently bad or that the manga itself is lacking, as today's example proves.
YOU'RE MY PET (Kimi wa Petto), by Yayoi Ogawa. First published in 2000 and first published in North America in 2004.
Sumire seemingly has it all: a great college education, a job as a journalist at a high-profile newspaper, and the tall, stately look of a model. Too bad then that she's just been demoted from the politics section to the lifestyle page, her fiance dumped her for his mistress, and her coworkers are convinced that she's a stuck-up ice queen who deserves what she gets.
Then she finds a boy in a box.
The boy in question, a teenaged runaway, likes the attention she gives him (along with her cooking) and begs her to let him stay. She agrees, on one condition: that he serve as her pet. They won't be dating, but she will provide him with a place to stay, food to eat, and as much attention and affection as he can tolerate. He won't provide her with his actual name, so she dubs him "Momo" after a former pet. Their strange arrangement seems to be working for a while until Sumire's old college friend Hasumi comes back into her life looking to rekindle their relationship. Can she maintain a relationship while keeping Momo a secret?