Hello Rita,
I, also, use pieces of stabilizer for projects. I keep a zip-lock bag of "left-over" pieces of stabilizer for each type and label as such. I overlap the pieces and actually keep this in mind when embroidering. I also do this with the water soluble stabilizer on top of a project. Collecting these pieces comes in handy. You can actually get some good-size pieces for little projects.
After a project is completed, I would cut away the excess and suddenly realized that I had a whole lot of left overs. I know the "purists of machine embroidery" are probably cringing right now. But between being a quilter (we never throw away anything larger than 1") and, basically, being cheap! For me, stabilizer must be ordered online.
Also, like the other comment to you, I also spray my pieces with fabric sizing or a light spray starch (usually lavender). Iron all the layers together and then hoop or work outside the hoop. It works out well. I don't spray bulky items such as towels, robes.
Joan/NJ