The death of animals is not a result of animals “sinning”. They are acting on instinct, doing what is possible. But the death of animals, especially through predation, with the accompaniment of pain, fright, fear, destruction, seems to be a result of an imperfection, which includes the death and competition within the biome for space, priority, power, dominance. Scripture talks about the lion laying down with the lamb, and the child with the poisonous snake… this seems to be an ideal, a sought after state of being, so that not only humans, but all of creation will be redeemed and renewed: paradise renewed.
Physical death is natural to us, because we are used to it, just like we are used to injury, disease, competition, strife, pain, and sin in general. But we cannot equate “natural” to “good”. Scripture indicates that sin caused death. But scripture also indicates that one particular sin (such as that of a blind person) did not cause that person’s blindness. Sin changed what was good, into something not so good. This happened both in human relationship to God, and in the relationship of man with nature, and nature with nature.