Everyone has these little accidents, no matter how much care you take. It is a fact of life. What you need to do is reduce the risk down to the lowest possible level.
But there is a big difference between having your little finger ache for a few days, and having it missing forever, and I have seen it happen before my own eyes, but it happened so fast, I couldn't prevent it.
It wasn't a machining accident, but a chap sticking his finger into where it wasn't wanted. The only problem was, he wanted the finger, but due to the way it was chewed up and spat out by the engine cooling fan, there wasn't enough big bits to be stuck back on.
So always remember, ACCIDENTS DON'T HAPPEN, THEY ARE CAUSED.
John