It looks like the applique was done directly onto the background fabric without cutting away any of the background fabric behind the applique. Is this correct? I also see no batting coming through the background fabric. Do you feel the background fabric remains intact?
If this is correct, then it seems the structural integrity of the quilt remains safe and that the applique, while damaged, is merely decorative. Because the quilt has such sentimental value, you should definitely consult with your friend on how she feels about using it. Personally, I would feel fine using the quilt since the background fabric keeps the batting safely enclosed. I would want to keep the quilt as close to how the person who made it as possible if it were me, but that is totally up to your friend.
I've also seen suggested to cover the torn parts with something like tulle to try to protect it some? But again, in this case, it seems you would only be protecting the decorative aspect of the appliques, and not because it was actually because the quilt was so damaged it was unusable. I believe it is still very functional, as long as the background fabric remains intact. If your friend prefers a new applique, you can also try to match the fabric and replace
