The practice just about everywhere is that horses are purchased right before a claiming race, and immediately become the property of their new owner—even if the horse breaks down and dies. This has been causing problems, especially at Aqueduct Racetrack, where the Winter Meet death toll is nearing 20.
In response, regulators in New York have passed a rule declaring any claims on dead horses null and void. It's valid at all NYRA tracks for 90 days, and may become permanent. The rule exists not to avoid punishing the owners of the newly deceased horses, but to deter the entry of at-risk animals in races in the first place.