Sometimes I stitch around the applique, just inside the stitching line, and then proceed to do needleturn applique. That way there is a row of stitching that keeps the corners from raveling and I have a line to follow.
I will also sew a lightweight piece of interfacing or fabric , right sides together, and turn by cutting a small "slice" in the back of the applique. Then I press, and it's all ready to be appliqued, without any problems of fraying.