Originally Posted by NEPEANDOGS
Does anyone know of such an organization?
Yes, most rescues. You can set up an appointment with a director and get/give all the info you need (please thoroughly research the rescues though). Then an appointment with your notary to finalize your wishes.
Many rescues don't run out of a shelter facility and have foster homes that take in senior dogs. Personally, I've already been asked to care for a past foster if something unforeseen should happen to her owner.
With careful planning, you can ensure your pets will be well taken care of and loved.