I think I would take the duck off and appliqué something else. I would be concerned the duck may have more issues as it is washed again.

How about a low umbrella sort of like a Sunbonnet Sue's? Though I agree with deedum - only if the rest of the duck is more stable.

The hat and egg shell sound like good fixes.

I agree, put a cute hat on him. It will be adorable.

I think the reason of the shredding might be the fabric you used; I sort of see that the fabric is not smooth on the chest of the duck. Is the yellow fabric the same as any other used in the blanket?
I have this set of applique animals and embroidered them once. What you can do is embroider the appliqued duck on a soluble stabilizer or a tear away and then applique by hand the entire shape on top of the one you have. It might be a little bit bulky so if I were you I would take the yellow fabric with sharp scissors and then applique. Don't get discouraged, remember that just you will notice any imperfection. I think the blanket is very cute and will be loved.
andrea

Bonnet for a girl, hat for a boy, broken egg shell if you don't know!!! Sooooo cute!!

What a shame - such a cute quilt. But be glad you discovered the problem yourself and not the new mother when she first washed it. She would probably feel awful that she "ruined" it. I'd use different fabric for the applique and maybe handsew in a new duck after removing the damaged one. It's odd that it reacted that way, but it likely will have more issues when it's washed again, if you leave the duck. His tummy looks as though it's pulling away also.

I would put a hat on the duck and hopefully that will be a "meant to be" fix.

I agree with those suggesting you remove the duck totally and applique one from a different fabric. If the fabric is so fragile with a first wash it won't hold up when gifted. Very cute quilt!

I love the suggestions so far. You could also simply make another ducky block, carefully cut out the old one, and hand sew the new one in place.

One of the problems with using a close satin stitch is that it tends to "cut" the fabric. Looks like this is what happened to your duck; the fabric was weakened by the stitching and pulled away from the stitches. Next time you might want to use a fusible (I like Misty Fuse because it doesn't make the fabric stiff) and a satin stitch that is wider and not so close together.

Also, did you was it in a top loader? The middle agitator is rough on fabric, especially when a fold gets caught. A front-loading washing machine is more gentle.

Edit: I didn't realize that these are machine embroidery. Not sure my comments about the satin stitching apply, as I do not have an embroidery machine.