My dog is always interested in fur & hairs, likes to sniff at packages when they arrive too, but hasn't damaged anything. She's a good dog!
I have a sister in law who lives with us. She has a cat. He's still a kitten, but likes to roam around my basement, which is where my tying room is located.
He likes to carry things up stairs. Yesterday, my sister in law brought me a spool of thread that he had snitched. Again, so far nothing damaged, but I'm keeping a close eye on the little bugger!