I put muslin behind my embroidered blocks so that the embroidery floss doesn't show through the back. It has nothing to do with reinforcement.

If the fabric is lighter wt ( since it is white and things tend to show thru) I do sometimes ur a light wt fusible to help hold the threads, as Grandbysquilts suggests. ButI have also, backed the block with another piece of white muslim just because I dont like seeing the seams/thread,etc thru the top....
I"m rather wierd tho..... lol

lol..I have no trouble being weird! Thanks everyone!

i've done quite a few embroidered block quilts- i put a layer of muslin behind my square (before) i embroider them- this keeps the threads on the back from showing through on the front-
it wouldn't make much difference if the embroidery is already done.

I have quilted two heavily embroidered quilts for the elderly friend of a friend, and they were reinforced with sew in stabiliser. The quilts were so heavy I would not like to sleep under them!

I quilted aroung the embroidery as close as I could, and heavily quilted the areas that were 'empty', and they seem as though nothing will ever come undone.

if they were hand work, maybe, but machine embroidered, NO...they will be fine!