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The title line sounds a bit confusing. I apologize for that.
Say I'm on my xbox one but I'm playing an xbox 360 game such as borderlands 2.
Is it possible to use a wired 360 controller for gameplay?
Nope. The only way you could do that is if you was streaming the xbox through your PC using the xbox app and used the xbox 360 controller that way.
Otherwise, XboxOne pad only i'm afraid.