Stroke survivor can benefit of mirror box therapy even in the absent of voluntary movement. Research as shown at the mirror neuron system respond not only during action execution, but also during observation of actions being performed. So by watching the reflection of the unaffected limb in a mirror the mirror neurons for the affected side can be activated.
For more information about mirror neurons see links below or just google mirror neurons
http://en.wikipedia.org/wiki/Mirror_neuron
http://www.edge.org/3rd_culture/ramachandran06/ramachandran06_index.html
http://www.sfn.org/index.cfm?pagename=brainBriefings_MirrorNeurons