You are off a bit. Fenrir is not Loki's pet, but his oldest son. When the other gods found out that he would be responsible for the destruction of the world, the gods tried to chain him down. Since Fenrir is a giant wolf, that didn't work out too well. The gods then used a special "chain" made by dwarven magic, which worked like a charm (not counting the fact that Tyr, god of war, had his hand bit of by Fenrir).
On the day of Ragnarok, Fenrir would break his chain and kill Odin, but would then be killed by Odin's son, Vidar.
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