What can I do to get rid of this cat that my parents love but is unhealthy for them?

My parents next door neighbors bought this cat at one point (I assume) and then stopped caring for it. They didn’t really feed him, so he would wander around the neighborhood and would frequently come to my parents house and they would feed him. The neighbors ended up moving, didn’t want the cat anymore and my parents “adopted” him. My parents are giving and loving people (I myself am an adopted child), but this cat is unhealthy for them. They are getting old, in a few years they will be in their 70’s. This cat will wake them up in the middle of the night b/c he wants to be fed, or he wants to go out. They are on over a dozen medications for various health reasons, they don’t need to be woken up at the middle of the night. They would never agree to giving him away, they are the type of people that would sacrifice their own health to take care of someone else, or even a cat. Part of me wants to take the cat to the spca and tell them it ran away, but that would be wrong. I tell them how I feel but like I said they are too giving and loving to let him go. What can I do?