See this previous answer I wrote. Short version: Little Boy would have likely had a nuclear yield no matter what, it was just too much highly-enriched uranium in one place. Fat Man could have detonated improperly but it would have spread plutonium all over the place. It would not have been easy for Japan to recover it, and certainly not easy for them to have used it (they'd have to recreate the implosion design, which was not easy). There were no contingency plans in place that I have ever heard of. By the time they dropped the bombs they had sufficient understanding of the weapons to know that there were really no conditions that would be recoverable.