This is probably a stupid question, but I'm curious now after I opened the refrigerator looking for eggs to make a cake and there was only one and it was cooked. Is there any way to undo that, whether at home or an industrial way?
No, there is no way you could do this in a kitchen. The process of denaturation is usually considered irreversible, a boiled egg stays boiled.
Ok, it is possible to un-denaturize proteins if you have the right chemicals and a fast centrifuge available and it earned Colin Raston and his team an Ig Nobel Prize. But even they can't "unboil" your boiled egg from the fridge yet.
So it seems you either have to quickly perfect the method of Colin Raston (and possibly earn an award or two on the way) or schedule a trip to the store. Alternative approaches are asking your friendly neighbours for an egg or two, choosing a cake recipe without eggs or postponing the baking project.
Yes its possible.
But its not easy - the team who first did it won an Ignoble prize - you can see it here
The simple and practical answer is no. You will have to go buy another egg!