It sounds like you want to use welt cord. That's typically attached to one face fabric, then the other with the item inside-out, then the item reversed.
If you wanted to do that on a quilted item, you'd have to trim it to the exact measurements before quilting, attach it as noted, and then "birth" the quilt, then quilt it.
Look at some home dec sites to see how welt cord is applied.
BTW, most decorative upholstery cording is not machine washable. If you make your own welt cord cover with quilting fabric it would be.
Last edited by mkc; 09-23-2024 at 06:36 PM.