Rabbits might eat rat poison, but they won’t eat rats. Rabbits are vegetarians and so the question of their eating poisoned rats will not arise. If rat poison is put at the backyard and the rabbits have an access to the area then the possibility of their consuming the poison exists. Consumption of rat poison can cause coagulopathy wherein the blood does not clot properly. This is a common type of symptom seen in cases of rat poisoning of rabbits.