If someone has power of attorney for the deceased owner and is acting on his/her behalf, or if the executor is acting upon a specific request within the will, you can consider doing the procedure as long as a legal document verifies the deceased owner's designation of the duly authorized agent.  If no verification document exists, and the person is not authorized in the patient records to make treatment decisions for the animal, then it would be wise not to perform the euthanasia. 


Regarding whether healthy animals should be euthanized if such a request is made and there is no compelling medical reason for the euthanasia, the procedure is not considered animal cruelty provided it is performed in accordance with the AVMA’s guidelines on humane euthanasia.  However, any veterinarian who objects to a euthanasia request is not obligated to perform the procedure; in such cases, the veterinarian irequired to return the animal tthe owner (or owners agent)


If the owner or agent refuses to take the animal back, you could have it declared an abandoned animal (see procedure at https://www.nysvms.org/resource/collection/E45CA734-8B73-4255-B861-5BED0FCBBAC9/abandonedanimals.pdf) and eventually deliver it to a shelter, where it can be put up for adoption or euthanized after 5 days.