OK, not sure exactly how limited you mean by your innacurate description but it's enough to give an idea. Try side lying on better side with enough pillows etc under the stroke arm to support it without forcing movement in directions it can't go in, and in a "neutral" position. Support top leg with pillows, therapy block or whatever. Try raising awareness of thorax and scapula by hands on stuff. "mark" the outline of scapula with your fingers; have your hands on the thorax to feel and reinforce movements of respiration. Passive movements of scapula. See what happens to the rest of the upper limb. From in front of patient, one hand on upper humerus and helping with maintaining slight approximation and slight ex. rotation (just whats possible) of GH joint, assist scapula with arm protraction..then retraction, maybe some is possible. See what assisted movements and gentle stretches of the arm are possible in whatever position of the body is best for lowering the increased tone.
I've also tried unilateral PA's in side lying with stroke patients for Thoracic mobilisation and increased sensory input. Trunk movements in side lying might be very suitable for loosening the arm. Rotation thorax/pelvis I'm sure you've tried already. As for fingers and hand, go gently for the small amount of extension/flexion you have and repeat it. Sometimes by "marking" thenar and hypothenar eminence in longitudinal direction with a spatula or similar one can get a bit of release in the hand. Or stimulation of inner small finger side of hand. Gemtle massage and squeezing of thumb adductors and massage of space between metacarpals can help as well. Depends on patient and pain reactions. Don't give the arm up completely as weird feedback from arm influences trunk and the rest but it sounds pretty bad and I guess won't be functional. I wouldn't start on serial casting either. Be careful with shoulder to avoid a nasty painful one, maybe relatives should also take care whilst dressing and doing transfers. Just do what you can, remember. No quick fixes!