Sometimes, instead of replacing or covering a damaged or fragile patch with a replacement, the patch is stabilized and protected with crepeline. This is a choice that might be made when a particular fabric in the quilt has significance to the owner — a favorite dressmaking fabric, for example, or an apron remnant.
Crepeline is a very fine see-through silk material that is used in a variety of conservation, restoration, and artistic applications. Individual threads in the material are smaller in diameter than a human hair.
It is laid in side by side, just as I explained in an earlier post.
Very fine stitches are taken in order to minimize their appearance against the fabric. This is the view through my magnifying lenses:
Two sides are laid in:
Here’s another magnified view of the stitching line:
Here’s a normal view:
And here’s the finished product. The fragile fabric is protected against casual snags by rings or fingernails, and the owner can continue to enjoy the memory of this fabric. 
Rumen Nation 
amazing job. quite the interesting assortment of fabrics in that last pic…
This is SO informative, thank you!
Based on your tutorials I think I’ll just rip out or work around the deteriorating patches on my inherited crazy quilts! Or hire someone to fix them for me… ;- )
So, did you turn the edge under like applique or did you just lay it flat out and stitch it down? My toile looks very much like your crepeline.
It depends on the final use for the object. For personal family items, they tend to prefer I turn under. It can be a pain.