Your company seems to be ethical and empathetic and has gone out of its way to accommodate this employee. That's great, but .....
His performance was unsatisfactory even before he was injured. How did his references check out when he applied for the position?
From the little gleamed from what you write, and obviously not knowing all the facts, my gut feel is that far from being an asset he is a liability, and the longer he stays the bigger a problem he will become. It really seems he needs a salary, but a job, not so much.
Consult an experienced labour lawyer, give him all the facts and follow his advice. He will have dealt with many similar cases before.
Record and note dates, times and details of every meeting and discussion with the employee, I suspect that if you don't do this one by the book he will end up suing you.