Will squeezing a ball help my hand get better after stroke or brain injury?

Like so many things in neurologic rehabilitation, the answer to this question is, maybe, it depends.  In its simplest form, physical recovery from stroke and brain injury boils down to this.  Whatever you see too much of, do the opposite.  If you have an already tight hand that is closing into a fist, practicing squeezing a ball will likely give you a tighter, more closed fist and may make it harder for you to develop the ability to open your hand and let go of the ball.  In this case, a stretching program combined with an appropriate splint to keep your hand open may be more appropriate and may help you work toward being able to open your hand.  Over time, squeezing a ball may become part of your rehab program if you need to develop strength and the ability to hold and manipulate things with your hand.  Your therapist can help guide you to the appropriate activity or exercise at the right phase of your recovery.