Final answer:
Beowulf would likely request that his sword and armor be returned to his family if he fails, as this act would honor his bravery and serve as a remembrance for his family.
Step-by-step explanation:
What Beowulf requests if he fails in his battle against the dragon is depicted in the epic poem 'Beowulf.' Based on the known elements of the poem, if Beowulf were to fail in his quest against Grendel or the dragon, the most appropriate action from the given options would likely be (b) Return his sword and armor to his family. This is based on the tradition of the time and the cultural practices depicted within the poem. It would serve as a token of his bravery and as a remembrance for his family of his heroic efforts and ultimate sacrifice.