Pixey, yes it does stay stable after pre shrinking it. However, I find that it's still rather sensitive to heat, so be careful what it's used on.
Over the years I discovered that I don't like it much except for on items that won't see an iron! It's often recommended for t-shirts and other clothing, but I was never really thrilled with the results.
My experience is that I do this with clothing: I stiffen up the fabric real good and use either a Tear Away or a Wash Away. And because I digitize I often-times will either create my own designs or alter a purchased design to assure that it isn't too stitch dense for the fabric/clothing. I like my embroidered clothing to maintain a nice drape and not be stiff behind the embroidery.
For items that don't need to be drapey, I will fuse on a lightweight interfacing product as has been mentioned by Jane and Patricia in this conversation. (Shape Flex, Knit Fuse, etc.)
One other thing that I try to remember is what our old friend and master digitizer Maggie Cooper used to say, "If it needs more than one layer of stabilizer, there's something wrong with the digitizing!"
Remember that if you're embroidering clothing, and you have 2 or more layers of TearAway stabilizer under the stitches, those stitches live there forever, making the garment stiff.
I once purchased a beautiful embroidered dress from a high end store. I knew nothing about machine embroidery at the time but realize now that the stabilizer was a PolyMesh. I assumed that with washing the embroidered area would soften up. It never did. I even trimmed out as much of the PolyMesh as I could, but to no avail. It was an expensive lesson, but one that in years to come helped me to discern a better use of stabilizers!