Of course it can.
Its called secondary poisoining.
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4c) Secondary poisoning:
Secondary poisoning is poisoning that occurs when a predatory carnivorous or omnivorous animal (domestic pet or wild animal) consumes the carcass of a poisoned animal and becomes secondarily poisoned by the same toxin that killed the first animal. Although just as likely to consume ratbaits directly, dogs may become poisoned by eating sickly or deceased mice and rats and scavenging the carcasses of poisoned larger animals. Cats, in particular, are much more likely to become secondarily poisoned by anticoagulant rodenticides than they are to consume a poison bait directly. This is because they are keen hunters of rodents (poison-weakened rodents pose an easy target) and because their finicky, selective tastes makes them less inclined to eat unfamiliar substances like pelleted or wax-block baits. The risk of secondary poisoning of cats and dogs is greatly increased with the anticoagulant-type rodenticides because weak, bleeding, dehydrated mice and rats often come out into the open to look for water: this makes them easy pickings for alert felines and canines.
Which poisons pose greatest risk of secondary toxicity?
Secondary poisoning is a particular risk with the second generation, single feed rodenticides (e.g. bromadiolone, brodifacoum, difethialone) because these poisons are stored for long periods of time in the rodent's liver and other tissues; because they are very potent (small doses are capable of killing large animals) and because, at a single feeding, a mouse or rat can potentially consume enough poison to kill not only itself, but a secondary predator. Strychnine also poses a high risk of secondary poisoning of predators and scavengers, as do long-lasting, high-residue poisons such as arsenic and thallium. The risk of secondary poisoning of domestic pets and wildlife is greatly reduced with the multiple-feed, first-generation anticoagulant rodenticides because mice and rats have to feed on these poisons several times in order to ingest enough to kill them: a dose of poison that is far under the amount required to kill a much larger dog or cat. The risk of secondary poisoning is also low with vitamin D analogue poisons, metal phosphide poisons and cyanide-based poisons.
Secondary poisoning is also a risk with regard to the active hunting and consumption of 'healthy-looking' wild animals (e.g. deer) in reserves and consumption of meat-animals in farmland where poisoning is occurring. Certain poisons (especially the second-generation anticoagulant rodenticides) are high residue, difficult to break-down poisons, which build up in soils and waterways over time. These residues find their way into the livers, fat and organs of herbivorous animals grazing and drinking in these regions and accumulate to high levels within these organs. Humans, domestic carnivores and wild animal carnivores that hunt living, poison-contaminated wild herbivores (e.g. deer in New Zealand) or farm animals and consume the meat and organs (especially the liver) of these asymptomatic animals may potentially consume enough toxic residues to become poisoned. The risk of build-up of poisonous residues in the organs of live prey animals is highest with the second generation anticoagulant rodenticides and certain heavy-metal poisons such as arsenic and thallium. Although diphacinone is categorised as a 'second-generation' product in terms of veterinary treatment protocols, it is actually favoured in many wild animal and farm pest (e.g. voles, gophers) control programmes because it poses a low residue risk, lower meat accumulation risk and low environmental contamination risk (i.e. it degrades quickly, leaving minimal traces). Likewise, cholecalciferol, zinc phosphide and cyanide-based poisons are also favoured in such programs because they too pose a lower risk of tissue residues and environmental persistence.
A final note, it is also possible for predatory domestic pets and wild animals to become poisoned following the consumption of vomitus or stomach contents from recently-deceased rodents and feral animals. The stomach contents (broken down vegetables and plant matter) are a favoured source of vitamin and mineral nutrition for carnivorous hunters. With rapid-kill baits (baits that kill within minutes to hours of consumption), the stomach contents of deceased pest animals can be full of poison pellets, poisoned meat or poisoned vegetable matter and, consequently, pose a huge risk to the predator. Rapid-kill baits in which secondary consumption stomach contents can be a poison issue include: strychnine, ANTU, cyanide, arsenic and 1080 baits. Vitamin D analogues and anticoagulant rodenticide poisons, in contrast, tend to exert their effects over a period of days (2-5 days) and, by the time the animal dies, its intestinal tract is normally clear of the poison and thus does not pose a risk of predator toxicosis.