I can move you here and there, but I always stay in the same place.

I leave my mark on stone and steel, on every wound that’s learned to heal. Though none can stop or turn me back, I quietly remain on an ever moving track.

I live off another, Stealing life, I grow so strong, Host becomes my grave. What am I?

A wanderer in the furthest waste. Felines, tradition says, it will erase.

Bound together at birth, cotton, wool, maybe cashmere if your well off. Good luck keeping me with my counterpart after wash!