Most of the people she kills, she straight-up murders. Copperhead murdered and ate some people, and Kate prosecuted, and lost the case. The defense was, basically, "he's not culpable, killing people is in his nature." Then, IIRC, he escaped from the van on the way to whatever cushy rehab place he was going to, and Kate decided, "well, if he's just been legally declared a rabid dog, might as well treat him like one."