Another possible interpretation of the titular question: an amino acid sequence with a fixed stable functional configuration but one that it cannot naturally reach because some intermediate stage of the folding is forbidden. I suspect such a thing is possible, and one might even be able to synthesize the final structure (in pieces, perhaps?).
My first thought was knotted proteins, but somehow those actually exist in nature (how?!): link.
Another possible interpretation of the titular question: an amino acid sequence with a fixed stable functional configuration but one that it cannot naturally reach because some intermediate stage of the folding is forbidden. I suspect such a thing is possible, and one might even be able to synthesize the final structure (in pieces, perhaps?).
My first thought was knotted proteins, but somehow those actually exist in nature (how?!): link.