In Beowulf, are the Geats spurred to repentence by their sorrow at Beowulf's death or by the prophecies of the Geatish woman in the final stanza?
Different translations of Beowulf will give different interpretations for the motivations of various characters. In the last part of the story, when Beowulf once again proves his worth as king and leader by facing the dragon alone, the other Geats flee and prove themselves unworthy both of leadership and of Beowulf's love (although Wiglaf proves himself worthy by remaining instead of running). A portion of the original text where a woman (possibly Beowulf's widow) may have been lost, and is referred to parenthetically in some translations:
Wailing her woe, the widow old,
her hair upbound, for Beowulf’s death
sung in her sorrow, and said full oft
she dreaded the doleful days to come,
deaths enow, and doom of battle,
(gutenberg.org, translated by Gummere)
Likewise, a dirge of sorrow [was sung for Beowulf by a woman; with hair braided up, she repeatedly said that she dreaded the evil days to come—days full of death, bloodshed, the horror of warriors, and captivity.]
Lesslie Hall's exhaustive translation leaves this portion out entirely, indicating that the original text is lost.
The implication is that the Geats are destined for terrible events in their future, as the Swedes and other forces band together to conquer and then control their territory. Without Beowulf and his leadership, the Geats will be unable to fight back and defeat oncoming threats; they have had this proven since none of them save Wiglaf were brave enough to face the dragon. It is likely, since they mourn Beowulf's death after Wiglaf's remonstration, that the Geats as a whole are ashamed of their actions and failure to help Beowulf in his last hours; they know that without him they are likely to be conquered by outside forces. Although Beowulf himself considered Wiglaf a worthy successor, Wiglaf does not seem to share that view; instead, the messenger sent by Wiglaf spreads this depressing prophecy to all who listen. It is possible that their shame will spur the Geats to new bravery, and the dirge sung by the woman at Beowulf's funeral is simply a reflection of that shame. However, if their shame is forgotten, the Geats will fall to a determined outside force, proving Wiglaf correct in his assumptions.