Love lost, heart broken.
The '6 word sad story' I think of is 'Saw future, future wasn't there.' It might be about a person who had planned their whole life. They had a clear vision of what their future would be like. But then, due to unforeseen circumstances like an accident or a major setback in their career, that future they had envisioned vanished. It shows how fragile our plans can be.
Some words for a sad story could be 'tragic', 'heartbreaking' or 'melancholic'.
Gift, rejected, sad. Imagine you put a lot of effort into a gift for someone. It could be a handmade item or something you carefully selected. But then that person rejects the gift. It makes you feel sad because not only is the gift not appreciated, but also your feelings behind it are ignored.
Melancholy tale could be used. It suggests a story that evokes a sense of sadness and pensiveness.