/u/restricteddata answered this in his excellent AMA on the Manhattan Project last week:

(/u/mhawks asked: What if either of the bombs dropped and failed to detonate? Was there a failsafe? Or would the impact detonate the bomb anyway?)

In the case of the uranium bomb, Little Boy, it was thought that the impact would probably cause it to detonate anyway. It was a very simple mechanism.

In the case of the plutonium bomb, Fat Man, there were four contact fuzes on the nose. If it hit the ground, its high explosives would detonate and disperse the plutonium, making it basically a "dirty bomb." It would not undergo a full nuclear detonation. That would not be ideal but it would prevent the Japanese from recovering the bomb fuel.

These were the only fail-safes in place, and to my knowledge they made no further plans about it.

Just as a follow-up question, would Japan have had the capability to exploit the technology at all even if an intact nuclear bomb were to fall into their hands?

Follow up: what failsafes were created on the years after, and which may be in place for the current nuclear ogives, if any?

Follow-up: If the Japanese didn't surrender after the second bomb, what was the allies' plan? Wait to make more atomic weapons, invasion of the mainland islands, more conventional bombing, or all three?