Answer: You should try to involve him/her the most in all the job task, so that he/she can grow in the job. Him/her should always be assisted while performing a task, for improvement. You can also identify trainings that can help to improve the worker's skills on the job.
You must not complain about the worker's unproductiveness always. You must not capitalize on the worker's weakness always. You must not report the worker's unproductiveness to the management to bring in a new person, instead let the management know that your coworker needs some training for improvement on the teams performance.
Your coworker is your team and you have to identify his strength and capitalize on it always, as he/she develop his/her weakness to strength.