Definitely! If they do eat some and you notice it um... hanging out... just trim it close with a pair of scissors and pay attention to see if your pet is acting off in any way and you need to call a vet.

Never pull anything string-like out of either end of an animal or human since that can cause very nasty internal injury. This is more of a problem with cats because their tongues make it very hard for them not to swallow a string-like object if they get it in their mouth.