One way to stabilize the amount of movement when embroidering fleece garments is to connect the embroidery backing to the underside of the fleece. Use an adhesive to stick the backing on the fleece, or use an adhesive backing.
Tearaway adhesive backings work well on smaller designs that do not have many filled areas. For designs with large elements of fill stitches, use a lightweight cutaway wet laid (or poly mesh) stabilizer and a light misting of an embroidery adhesive.
Also, for soft, loose, loopy or nappy fleece fabrics, adding a soluble topping will help the stitches form above the surface of the fabric, rather than sink down into the fabric.