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THe Creature wants Victor to live alone just like he has been doing. He kills Elizabeth as his final act of revenge; the creature wants Victor to experience a similar pain of loneliness and isolation as was bequeathed to him. THe creature no longer dreams of contentment or happiness. He only seeks to quench his thrust to make Victor suffer again and again in perpetuity.
I meant quench his "thirst". Damn auto-correct!