I leave it on some of my towels without problems. I don't know if it will "shed" on clothing items or not though. I think if it is a decent quality you will be fine.

This might help you. I was having a hard time figuring out what stabilizer I had in my hands once too often. I made tags identifying my stabilizer by type and weight and used headband elastics from the dollar store so I could slip each one over the correct roll. I would recommend that you use velcro rather than elastic in hindsight. Now it takes me seconds to find what I want. Sorry I can't help you with any potential consequences.

I wouldn't think it would be a huge problem...I would think that eventually it would disintegrate with washings...and if it is something that will not be washed, then I can't think it would matter...

I have found the tearaway in ready-made clothes. There was no problem; I was just curious about how the embroidery looked on the other side and how it had been done. I also checked things we owned that had been in the washing machine and dryer when I first got interested in machine embroidery. No problems there, either. I hope all goes well for you.

I should have been more clear. I put the stabilizer inside a mug rug. So I'm concerned that it could wad up inside there. Guess I'll just wait and see.

You should be okay with a mug rug as long as the person who has it only washes with a damp rag - not in a washing machine.