Non-viable Industry with demand curve above supply curve
If we consider that no one wants an infinite number of any material thing other people can supply and that there are only a finite number of people/firms, the demand function should be bounded. That means that eventually the price people are willing to pay for one extra unit of the good will be zero, and assuming non-negative production costs at this point the supply curve will not be under the demand curve. So the situation you describe can only exist in theory.
However you can have examples where for large quantities the demand function is over the supply function, e.g., the market for ordinary air. People desperately need air (up to a limit), yet it can be supplied at zero cost (it is freely available, again up to a limit).