Maybe it's something like 'film footage' or 'video capture'.
It could be 'novella'. A novella is longer than a short story but shorter than a novel, which might fit this crossword clue.
It could be 'yarn'. A yarn is often used to refer to a long, rambling, and perhaps even fictional story.
Another option could be 'parable'. Parables are short stories that convey a religious or moral lesson. While they are generally short, some parables can be more elaborate and thus considered a 'long short story' in relation to the crossword clue. Parables are found in many religious and cultural traditions, like in the Bible for example, and their length and complexity can differ.
Perhaps 'epic'. An epic is a long narrative that often involves many characters, complex plots and sub - plots, and a wide range of events. It can be a story of heroic deeds, like 'The Iliad' or 'The Odyssey' which are classic examples of long, involved stories.
It might also mean the highest level or floor in a building in some cases. Say, in a crossword that has a lot of architecture - related words. If the clue is something like 'Top Story in a Skyscraper', then it's about the topmost floor.
Novel. A novel is a long written story, which is a very common answer for a crossword clue like 'long story'.
It could be a word like 'plot' or 'tale'. Those are common terms associated with narratives and stories in crosswords.
A clue for a body of fiction could be 'fiction book' or 'imaginary tale'. It really depends on how the crossword setter wants to phrase it. Sometimes they might use a synonym or a more creative description to make it challenging.
Epics could also fit. Epics are long narrative poems or stories that often deal with heroic deeds and adventures, so they are a great match for the 'long stories' crossword clue. They usually have a complex plot and a large number of characters.
An innovative idea. Since 'novel' also means new and original, an innovative idea could fit the crossword clue. It could be a fresh concept in various fields like technology, art, or business.