Can a monk choose to eat only an animal or plant that had died naturally?

If someone hires a person to kill another and the plot is discovered, both the hired killer and the one who hired him will be arrested and imprisoned. Yet, somehow, if a monk eats food given by others, no negative kamma is created, even though the monk is aware of and complicit in the process of killing, i.e. he knows someone else had to do the killing of the plant or animal for his ultimate benefit, even if it wasn't explicitly killed for him. Even worse, someone whose profession involves the daily killing of animals as is the case in a slaughterhouse, has to bear the mental consequences of this daily ritual as well as its kammic consequences. Yet a monk can avoid all this simply by waiting for someone to put the dead animal in his bowl. The morality of this doesn't make sense. I would think the only morally harmless situation would be for a monk to only eat an animal or plant that had already died naturally, either by scavenging for it or waiting for another to do so on his behalf. Question: Can a monk choose to eat only an animal or plant that had died naturally? This either by scavenging on his own or by waiting for others to offer this to him?