My parents want to put one of our cats to sleep?

Sorry but there's no way to cope when its not a serious condition. Only monsters would rather get an animal euthanized than figure out the problem. They should either start the treatment again, take it back to the vet or find another solution. If its something serious that the cat is actually sick/suffering then yea, I can see putting it to sleep. Otherwise convenience euths are wrong and not all vets do that anyways because its highly frowned upon. Either way, it will always be hard to lose a pet after that many years.