A very troubling subject, Karen, but one that needs to be addressed. Since every pet is different, there is no one sized solution.
We added them into our wills, with funds set aside for their care, but that does not guarantee that they will go to a loving home. In our case, we do not have anyone that would be willing or able to take our kitties. That leaves our vet. Our senior cat has advanced Kidney disease and needs special care. Our younger cat is still extremely paranoid, and could not go to just any home.