The stabilizer is behind the entire square. It is the "light-easy tear" kind. I put the stabilizer behind it so the machine doesn't eat my fabric while I applique and so my square stays nice and flat. I use the easy tear kind because I generally don't wash my fabrics and so I don't like the idea of wetting my square to get rid it. This is the first time I have used blanket stitch and am finding that the stabilizer is getting caught up just a bit in the stitches so I can't get it totally out. :( There is only a tiny bit...so I'm hoping it's ok.
(edit: this is the first time I've actually washed my fabrics before use...but I am not used to, nor do I have the wash away stuff....)