Can a failed cupcake be incorpated into a new cupcake?

I don't think "twice-baked" cupcakes would work out well. I think you would need a lot more than one extra batch to blend with it to get a decent texture. Mixing them directly into the batter would probably just make some odd texture in places. It might not be that noticeable but I think it is going to degrade your new batch of cupcakes and risk having even more unfortunate cupcakes to figure out what to do with.

Instead of mixing them into the other cupcakes, I think you could crumble them and use them in another way. They would make a good crumb topping (for ice cream, muffins, some of the new cupcakes or a fruit cobbler), or use the crumbs with some binding agent (chocolate, peanut butter, cream cheese, jam, honey etc) and perhaps some dried fruit or nuts to make no-bake ball or bar cookies. A lot of those recipes start with something like vanilla wafers or shortbread cookies and you could replace those with the cupcake crumbs. I think these crumbs would be a little less firm than the cookie crumbs but it should still work.