How many stitches in the little bear? He is adorable. You can add a layer of fusible stabilizer to the back ground fabric. The fabric choice looks light weight and sheer. There are products from pellon, Floriani or Jenny Haskins.
https://www.rnkdistributing.com/reso...Stabilizer.pdf (Products on Pages 19-20).
I use a fusible on most of my EMB machine applique projects too. It stabilizes the applique piece of fabric, helps prevent fraying, and the pull from satin stitches too.