After the death of Arthur, Prince of Wales in 1502, Henry VII withdrew his sole surviving male heir from public life and kept him as a virtual prisoner so as to reduce the chances of him being injured or killed. After his wife's death, Henry VII was urged to re-marry for political reasons, but also for the possibility of siring additional heirs. He refused. Let's say the young Henry, Duke of Cornwall dies of plague or sweating sickness in around 1507. By this point he has likely not consummated his marriage to Catherine of Aragon (his brother's widow) and so has no children, legitimate or otherwise. This scenario therefore imagines Henry VII as the last surviving member of the Tudor dynasty - he is widowed, emotionally withdrawn, and becoming physically frail. All of his sons have died childless. What happens now? How would the succession likely unfold?