Hi Penny,
So far, everyone's advice is focusing on the embroidery (which of course is important) but doesn't necessarily solve the problem of sagging. That is only corrected with quilting. Any block not quilted will sag.
My experience has been to free motion around the design itself and then the block as usual. The larger the embroidery design, the more you need to think of putting some quilting into the design. (Even large appliques sag)
In the quilt you have shown, I cannot see any quilting. Nothing is holding the fabric to the batting and backing.
HTH,
Keitha