when you need to (or just want to) divide really hard bread without using your hands, I advise covering it with softer bread and then cutting through both. the soft bread helps keep it in place and catch crumbs.
if you've going to a fancy restaurant where the food is really good, but you're not allowed to lick you plate or pour the crumbs, you can bring your own bread in a paper bag. if the food was wet, you can just rub the bread on the stains. if the food was dry, you can put the bread in your mouth a bit first. it shouldn't be a very big bread. then you can eat it on the spot, or put it back in the bag to save for later.