He Won't Kill, She Won't Die

Kagami Tsutako has been obsessed with Ii Azami for 20 years. While stalking him one day, she encounters Ii Azami being hit by a car. When she discovers he has lost his memory as a result of the accident, she decides to claim they are lovers in order to fulfil her lifelong desire. As a result, as Tsutako repeatedly lies one after another they begin to increasingly escalate…

A girl is just 14 years old, but she endures a difficult life. Her parents abuse her at home and she is bullied by students at her school. She doesn't have a place where she can feel comfortable. One day, the girl is kidnapped by a man wearing a mask. The kidnapper names the girl Sachi, while wishing her to be happy. For the first time, Sachi can feel happiness.
(Source: kisskh)

In terms of story they are slightly different but are similar as to the relationship dynamics between the main couples and the psychological vibes. Both can be classified as romance that at some points have unsettling events happen between the couples.

Yomogida Fujiko is an office worker with an academic complex. She works hard and becomes a full-time employee at an insurance company, but because of her diligence, she is unable to refuse the work she is asked to do and accepts it with a smile on her face. One day, an elite company employee, Nishina Soma, moves into the room next door. Fujiko is soothed by the time she spends with her very kind and gentlemanly neighbor. But why did Nishina, a supposedly elite man, move into this shabby apartment, and why is he so kind to Fujiko...? It seems that Nishina, who does not speak much, is a stranger to Fujiko...?

Yomogida Fujiko is an office worker with an academic complex. She works hard and becomes a full-time employee at an insurance company, but because of her diligence, she is unable to refuse the work she is asked to do and accepts it with a smile on her face. One day, an elite company employee, Nishina Soma, moves into the room next door. Fujiko is soothed by the time she spends with her very kind and gentlemanly neighbor. But why did Nishina, a supposedly elite man, move into this shabby apartment, and why is he so kind to Fujiko...? It seems that Nishina, who does not speak much, is a stranger to Fujiko...?

Both are about two teenagers who both are lost and emotionally troubled and end up drawn to each other.

Sakuragi Shun is a salesman who works for a Sunbath Home Housing, a house manufacturing company. He enjoys a happy life at home with his wife and daughter. Due to a sudden personnel change, he was assigned to transfer to Kagoshima, a city he was familiar with from his junior high school days. There, for the first time in 17 years, he is reunited with his first love Takeda Hana. She works as a junior high school teacher, while her husband who works as first mate, spends most of the year at sea, so she usually lives alone. While reminiscing the bittersweet memories of their high school days together, a hidden Pandora's box begins to open...

Furthermore, sparks also fly with Katoyama Naoya, Shun's friend and former love rival from their junior high school days, who now works for another company in the same industry. Although Shun has a beloved wife, the flames of jealousy quietly flare up. Meanwhile, Sakuragi Shun's wife is trying to suppress her anxiety. Based on their phone calls and emails, she becomes suspicious that her husband is cheating on her, and in order to eliminate her fears, she takes a trip to visit him in Kagoshima. As the slight lies begin to pile up, the truth becomes complicated, and when the lies are exposed, how will the relationship between the four of them
change?

They're not exactly the same, but there's a hint of similarity. It's just this movie is like a thousand times more hardcore than He Won't Kill, She Won't Die and the roles are reversed. Watched the latter first, and really liked the concept. If you're open to "weird/strange" movies, then these two will fit your palate.

Both are movies about two isolated troubled young people - a rougher but good-hearted guy and a depressed girl - who bond and struggle to overcome the difficulties of their lives. While both have a tragic tone, BD has a much happier ending.