In what sense have the Danes and the Geats now “traded deaths”?(This happened somewhere in part 2, Grendel's Mother, of Beowulf.)
In order to answer this question, allow me to summarize what has happened prior to the action in question. The story of Beowulf opens with Hrothgar (a Dane) facing a horrible monster (Grendel). Grendel, despising anyone who praises God, attacks Heorot (Hrothgar's mead hall and place of worship). On the first night of his attack, Grendel murders thirty of Hrothgar's men. Night after night Grendel continues to attack Heorot until Hrothgar closes its doors.
Hearing about Hrothgar's troubles, Beowulf (a Geat) leaves his homelands to help Hrothgar. Feeling a debt is owed to the king (for taking care of his father), Beowulf offers Hrothgar his services to rid Heorot of the terrible monster. (Not only does Beowulf feel a debt must be repaid, he also is a true epic hero who seeks noble battles for God.) Beowulf, true to his word, kills Grendel and rids Heorot of the darkness.
Angered by her son's death, Grendel's mother attacks Heorot. While there, she takes the life of one of Hrothgar's man (Aeschere). Fleeing after ward, she goes back to her watery lair and places Aeschere's head upon a stake outside of her cavernous home. In this sense, Grendel's death is traded with a life of the Geats and the Danes (Aeschere).
Another way of looking at this question is where Beowulf looses one of his men during his battle with Grendel. In the opening of the story, many Dane's lives were taken. When Beowulf enters the tale, one of his own men is murdered. Therefore, one could look at this as the Danes and Geats "trading death" (although this happens prior to the entrance of Grendel's mother).