Is expiation required for someone who left a chicken with broken legs in a nearby plot of land with a little water, to avoid sin, based on the hadith: "A woman entered Hellfire because of a cat she tied up; she neither fed it nor left it to eat from the vermin of the earth"?

If chickens are among what can be benefited from by eating them, then they should be slaughtered and eaten. However, if they cannot be benefited from, then there is no harm in getting rid of them. It is permissible to destroy an animal that brings no benefit to avoid the burden of spending on it, just as Jabir (may Allah be pleased with him) did when he wanted to set free his camel that had become exhausted. As Sheikh Al-Uthaymeen (may Allah have mercy on him) mentioned, if an animal acquires a permanent defect that cannot be removed and it can no longer be benefited from, then it is permissible to destroy it in a way that provides it comfort, because keeping it and wasting money on it serves no purpose.