Don't do that. You should value yourself and your work.
At the end of your contract, polish up your resume, and create a nice list of projects where you can add value. Ask about having your contract renewed and be prepared to present both.
If your work has value to them, they should consider continuing your employment. If not, attempting to work for them for free will only create an awkward situation for you, your managers, and all the other employees on that team.
If this company can't pay you, find an opportunity that can. Businesses are not charity cases.