I have greens stealers. I'm generally good at keeping both cats away from my food, and I have a dedicated food trash (with a lid!) on my kitchen counter (that the cats aren't allowed on!), but if I leave the food trash lid open with romaine ribs or not good enough leaves, I will find chewed greens on the floor in the morning.
So I've actually started to just give them a piece of lettuce, already, if I'm having a hard time keeping them away from my salad plate. Athena grabbed a leaf off my daikon as I was slowly putting away fresh vegetables the other day.
My mother thinks I allow them to do all kinds of inappropriate things, but I'm glad I have a scratching post dining room table leg, I like them on the bathroom counter, and I don't have anything else on top of the television, so why shouldn't a cat go there?