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I am so sorry for your pet's situation! Yes, someone in your situation does have the right to seek compensation.
In the end, the pet is considered "chattel." What the groomer - the company - did was not provide the necessary care for the pet arguably, while the pet was in their care. This would be cause for negligence. The essential elements of actionable negligence are: (1) the existence of a duty owed to the complaining party; (2) a breach thereof; (3) a resulting injury; and (4) a proximate cause between the claimed breach and resulting injury. Hansen v. Washington Natural Gas Co., 95 Wn.2d 773, 776, 632 P.2d 504 (1981).
They damaged your chattel, meaning that they are liable for its "repair" or if it cannot be "repaired," then the price of a comparable item, much like if they had hit your vehicle.
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