We don't know for sure what is happening to your boxwood.  The yellowing foliage of the affected boxwood suggests two or three possibilities, but, there are also some unanswered questions.  For example, the fading color suggests a root problem, and the foliage on the 'protected' side nearer the healthy boxwood appears to be nice and green.  The  major trunk and the branches on the exposed side of the affected plant appear to have suffered some manual damage, from either human activity or from vole damage.  The plant seems to be leaning away from the foundation  of the house which also suggests the possibility of vole damage to the roots on that side fo the plant.  Vole damage could account for the yellowing of the leaves and the dieback of branches near the base of the plant.   You should examine the soil around the base of the shrub for loosened soil and/or entrance/exit holes in the area.  You could also grasp the shrub firmly and rock it back and forth, if it moves, you can assume vole damage.   If you suspect voles, you should place several mouse traps around the area that are baited with either peanut butter or a small piece of fruit.  If you successfully catch some, continue trapping since voles are colonizers. 
The wound near the base of the main trunk is also an entry point for insects and disease. If the plant continues to rapidly decline, it may be the result of Phytophthora fungal disease.  There is no treatment for this problem. 
Although we cannot determine the nature of the landscape adjacent to the affected side of the plant, it could be that the yellowing is the result of environmental conditions or other events that could have damaged the roots on that side of the plant.  Were other plants recently removed?  Has there been any construction adjacent to the plant?   
Please refer to the following publication:
http://extension.umd.edu/sites/default/files/_images/programs/hgic/Publications/HG52_IPM_Boxwood.pdf