Even if you have mice?
My cat was once in the living room playing with what I thought was a beetle. It turned out to be the tiniest little frog I've ever seen. I got it away from him, and noticed he (froggy) had a cat fur afro on his head. Couldn't let him go out like that, poor little guy, so I got some tweezers and pulled off the wig. A happy ending to what could have been a hairy demise.