Well, another term could be 'heartbreaking story'. A sad story often makes you feel sorrow, and a heartbreaking story has the same effect. It can break your heart when you hear about the misfortunes, losses or difficult situations in the story.
One common literary term for a sad part of a story is 'pathos'. It refers to the quality in a story, speech, or character that evokes feelings of pity, sympathy, and sorrow in the audience or reader.
A 'doleful story' can also be used instead of a sad story. The word 'doleful' has a connotation of sadness and grief. It makes you think of something that is mournful or depressing. For example, a story about a character who has lost everything - their family, their home, and their hope - can be described as a doleful story.
Well, 'mournful story' is one way. Also, 'gloomy yarn' and 'melancholic anecdote' can be used instead of'sad story'. These expressions not only convey the basic meaning of a sad story but also add a bit of a different nuance. For example, 'gloomy yarn' gives a sense of a story that is not just sad but also has a kind of dark and dreary atmosphere around it, like a story told on a foggy, cold night where everything seems a bit more desolate.
A melancholy narrative. It emphasizes the overall feeling of sadness and gloom in the story. Think of stories that deal with loss and heartbreak, they can be described as a melancholy narrative.