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Got a dumb question for you......
What is the brand of the "non-woven fusible" you use? There are SOOOO many types and choices that I sometimes wish Eleanor would package her own brand so I could get just what she's using! HA! The one I see Eleanor using doesn't appear to have a paper backing so I guess the fusible material is only on one side. HELP

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Fusible stabilizer is another name for fusible interfacing. I normally use Pellon brand as I am familiar with how it reacts to my sewing and pressing methods. Any of it will work. The fusible side is the one with the rough little glue dots. I use the sheerest weight one for this applique technique so you don't have bulky edge seams.

If your fabric is fraying, it is probably due to the fact that there is a bias area on your applique. This happens often when you are using curved pieces. EX: going from crosswise to lengthwise grain you have some bias areas. One solution to this: USE A VERY FINE LINE of fray check, or fabric glue on the very edge of the fabric, let it dry. Most dry clear, test a sample first. Most of the time the stitching will cover the fray check or fabric glue. Hope this helps!