So, in my circle of friends I've been known to often represent unpopular opinions. And since the last chapter there is this thing going on on tumblr which says that Law lost his will to live, and lost his hope, when he held his right shoulder and lowered his head…
I mean, really? Have you ever got your arm cut off? If that shouldn't be the case, than please let us quickly recapitulate what it means to have your arm cut off. First there’s the pain. That’s obviously the reason why Law held his right shoulder, because we humans tend to hold the spots that hurt. Secondly there’s the blood loss. Besides infections, this is the most common cause of death among amputation patients. And Law has lost a lot of blood because of all his injuries. (The fight on Green Bit, the shots and don’t forget the little scene in which Law’s torso got pierced by Doflamingo’s strings as he had tried to attack Trebol with his Injection.) So Law is probably in a condition where he feels dizzy and his vision starts to most likely be blurred. Besides that his whole body has to ache, and it costs a lot of energy to even hold his head high. Also humans tend to lower their heads when they feel pain in their bodies, because they feel a slight relief when they give some of their neck muscles a rest.
So, Law’s pose has obviously medical reasons, and isn't the result of him giving up his hope or his life.