Here is what the technique is, and here is how to use it.
The technique is simple. The teacher listens to a story that the student relates.
Then, the teacher relates the same story, but with a slightly more adaptive, solution oriented, mentally healthy, mature ending.
Then, the student retells the story, and the teacher repeats the process of upgrading the story in a more adaptive, appropriate ending.
That is all the work that you are required to do to use this technique effectively. Of course, you can adapt, embellish and elaborate the technique in any creative way that you desire.
There are no right or wrong ways to finish the story. The story is always a work in progress.
The technique also works well with teacher-written stories.
In this case, the teacher listens to issues, concerns or challenges that the students are facing. The teacher then writes all the retellings as stories for use in classroom reading, English, grammar, spelling, history, science, etc. You get the picture.
The stories can be about anything. Fables can be used to illustrate science principles or historical events or current events. (Human foibles haven't changed much in 2,500 years.)
The stories are powerful because students pay attention to the moral of these lessons whereas students "tune out" if they receive the same information while being lectured to.
It is also beneficial to begin mapping the language of Multiple Intelligences into the stories as you gain confidence in this technique.
This is just a matter of adding words to the story that associate with the five senses, i.e., touch, feeling, sight, sound, taste, smell.
Here, the teacher can allow students to brainstorm endings to the story in progress. Then, the last ending (the teacher's) turns out to be the most socially, emotionally, mentally healthy, or adaptive ending.
It is possible to use the same technique with textbook and adopted curriculum content, with students and teacher supplying better endings than the original author. However, there are two flaws with this approach:
It is difficult to find textbook stories that actually engage students
Teachers cannot collect the textbook stories (and the various endings and publish them) without permission of the original author
Reading material does not need to win the Nobel Prize for literature to engage students. Simple themes that allow students' imagination to escape the ordinary boxes of a typical school day thought are rewarding enough.