There is a wonderful product by RNK Distributing called "Quilters Select Fabric Prep". It is their new quilting products line endorsed by Alex Anderson. This is a feather weight fabric that fuses to the back of your fabric that adds a light support to the fabric to help relieve distortion, raveling, puckering and runs. (I am typing it right off the package). It is NOT a stableizer in the sense that you would use it in embroidery, but it supports your fabrics without adding bulk.
I fused it to the back of some silky fabric to add support before I cut it out. The item was to be embroidered, so I did use the appropriate stableizer and the jacket turned out beautiful. It was not stiff, but retained its softness and drape.
This can also be fused to the back of your finished machine embroidery to keep the "itchies" from little bellies when you embroider those dreaded baby onesies. Or any other itchy labels/seams/etc.