Yes, I find that the body does indeed often shift towards protection, whether it is by standing more on the non damaged limb, while holding the damaged one in easing patterns, or involuntarily tensing up to prevent movement at an inflammed irritable tissue site. That pattern then lasts years after the injury has gone, and the subconscious still carries on protecting and not chancing 'going back there' again. It's also often kinesthetic memory associated with accidents, and the pattern that caused the trauma, for example road accidents, and reliving the incident over and over and reproducing the movement memory trace over and over.
In my experience deep muscles relax to prevent micro movements, or any movement of joints, and superficial longer muscles take over. I wouldn't exactly call that 'hugging'.