I've had two experiences with senior dogs, including my own.
One was an old dog who I had watched multiple times before, and the owners were dropping him off before a week long trip to Mexico. The husband told me that if anything were to happen, they don't want any life saving measures taken. As a senior pet parent, I understood what he was trying to say and felt it a reasonable request, especially since they probably wouldn't have been reachable right away in the event that a quick decision for surgery, etc. needed to be made. But then he took it one step further and asked that I not tell them if anything happened to the dog "so it wouldn't upset his wife while they were on vacation". I must have looked shocked because he started back pedaling and saying of course I was welcome to contact them if anything happened. Thankfully the dog was fine and we had no reason to worry, but wow! At least he was up front and honest I guess?
Second time, I was going out of town and leaving my own senior dog in the care of my roommate (who I've lived with as long as I've had my dog - he was practically half hers). My boyfriend, referencing the previous owner, jokingly said "don't call us if he dies!" I told him to stop joking and told my roommate to of course call if anything happened. My dog died. We left Friday afternoon and when my roommate got home from work Saturday evening he had passed away in his sleep. Because of my boyfriend's (bad) joke, she was too scared to call and tell us so soon after our trip had started. It took her until Tuesday to work up the courage. In the end there's nothing that would have changed had she told us Saturday; she did everything I would have done. But I was surprised that she would take such an ill-timed joke from my boyfriend to heart, and wish I had been more convincing that she should never hesitate to contact me. In her defense though, she also knew we would be camping with friends until Tuesday and didn't want me to find out with so little privacy to grieve.
All this to say, I would never outright ask an owner what to do if their pet dies in your care, but most owners of senior pets are aware that the end is coming. If they don't present a game plan at drop off, always ask how to best reach them 'in case of emergency' or if there's someone you can call in case you can't get a hold of them. For all pets, senior or not, always know what vet or local emergency vet they would prefer you to take their animals in case anything were to happen.
RIP Scooby