During Ragnarok, Fenrir the wolf kills Odin and is then killed by Vidar. The Midgard Serpent Jormungandand and Thor kill each other.
What role does Hel, Loki's other child by Angrboda, play?
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None, as far as we know. She is not mentioned at all in either the poem Voluspa, which describes the event of Ragnarok, nor in Snorri's version of events in the Prose Edda. All he says is that when Loki arrives at the battle-field of Vigrid, he will have "all Hel's people with him". (Faulkes: 51)
After the Ragnarok, "Balder and Hod will arrive from Hel", where they were both living since their deaths earlier in the mythology. (Faulkes: 56) Snorri also says that there will be places for good and bad people after Ragnarok, the bad one being at Nastrands. Whether Hel will occupy it, or whether she died, is unknown.