Different manufacturers use different fibers. I would try and look up your brand to see its composition. I think some of them are polyester, so not paper.
There are several ways you can conserve stabilizer usage. Rather than cut squares or rectangles, cut strips of stabilizer the width of your hoop. Hoop as close to the end of the strip as possible, when you are done, carefully cut or tear out just the embroidery (basically make a hole in the stabilizer). Now you can move the strip up and hoop for the next embroidery. It's amazing how much you save this way. With water solubles, you can embroider your design, then cut around the finished design, making a window in your stabilizer. Now cut another small piece of stabilizer to cover the hole, overlapping about 1/2" all the way around. Some folks use a TINY bit of water & stick the patch in place. I just sew the patch in using a looong stitch length. This thread won't dissolve, but it's easily removed.