Broken crayons still colour..
I believe that this quote is stating that a broken person still functions. And in most cases they do, dysfunctionally maybe, but they usually continue to function.... until they don't.
A broken person is not living their life, they are merely existing.
I truly believe that keeping our issues under lock and key inside of us will manifest into illness. The illness may only be a 'warning' of sorts, to get you to pay attention to the buried issues or it may be a sudden exit point. The 'warning' is a second chance, an opportunity to work on your 'stuff' and find some forgiveness, resolution and gratitude.
I believe that we create disease for ourselves, by ourselves. We were born perfect and we are perfect; but keeping everything inside will cause stress and result in disease. Hanging on to anger and resentment will cause disease. Release is the answer. Release all the inner conflict, release the anger. Forgiveness, of others and of yourself, will open you up to healing. You WILL still be able to function, as a broken crayon, but what kind of life is that for you? Where is the joy? Work on whatever broke you in the first place, figure out what is the culprit and work on letting it go, release all the negativity, forgive whomever you need to and start to live your life as a WHOLE person.
This reminds me: A man was on the stage delivering a parable, with a $100.00 bill as the prop. He asked the audience who wanted the bill, and most put up their hands... He then took the bill and ripped it in half, crumpled it, threw it on the floor and stomped on it. Then he showed it to the audience crumpled, torn and dirty and asked who wanted it now. Most of the people just sat and looked at him. What he explained to them was; even though the $100.00 bill was torn, dirty and crumpled, this did not diminish it's value. It is still worth exactly what it was, brand new.
No matter how broken you are, you are still worth everything that the world and the universe has to offer.
Life may have beaten you up a bit, but it can never diminish your value.