The drama you're describing sounds like "Mr. Right" (or "Very Good Days"), a South Korean series. In this story, a successful CEO gets into a car accident and is presumed dead. However, a young woman inadvertently causes an accident that leads her to take care of him, and their relationship develops from there.
This kind of plot often involves themes of romance, healing, and personal growth. If you're looking for more specific details or recommendations, let me know!