One day, while Keiichiro is in a dump, he finds an abandoned helper robot. He believes she's broken and takes her to a repair shop, but they tell him that her model is too old and that the parts are no longer available. Keiichiro takes her home and leaves her in the bathroom before going to bed. When he wakes up, he finds the robot downstairs making him breakfast. However, she has no memory of who she is or what her life was like before she woke up that morning.
When she asks what her name is, Keiichiro names her Flower. He takes Flower around town and teaches her about money so she can do the shopping. After finding out that she has a terrible memory, he buys her a notebook where she can write down what happens during her day so she won't forget. They then go on to experience things that make every day fun for Flower. However, she notices that Keiichiro doesn't smile at all. Is there a way to bring back the happiness that she has seen in the old photos around the house?
Half-Broken Music Box was interesting. It reminded me a little bit of Planetarian, though I think the Planetarian anime left more of an impact on me. Half-Broken Music Box is a good slice-of-life anime. Judging from the art and descriptions I found online, I went into it thinking it was supposed to be an emotional anime like Anohana: The Flower We Saw That Day. While it didn't make me sad, I found it relaxing to watch.
The characters all dress modestly, though you do get a glimpse of a pornographic magazine when Flower is cleaning Keiichiro's bedroom. Besides that, it's a pretty wholesome anime. I would definitely recommend it if you're looking for something short and relaxing.