and if he didn't kill the animal, then it was already dead. death before the fall. (chances are it did not die directly because of the fall... that was adam's supposed fate. therefore logic would suggest it died before this alleged fall.)
Gen 1:31 And God saw every thing that he had made, and, behold, [it was] very good. And the evening and the morning were the sixth day.
this is what he said after he made man. every day prior to his making man, he said things were good. thus it can be assumed that man was the very part. but man being 'very good' does not mean immortal and perfect.