Hello, I'm a new(ish) groomer in the US who has been struggling lately working on elderly dogs who have little quality of life left - dogs who are in pain and can barely walk that the owner still clings to. I have a lot of compassion for the owner, who doesn't want to say goodbye, but when the dog is in my care the suffering is very hard to see. These are often repeat clientel. I do my best to make them comfy while they're with me, but is there a time I should send them to a vet for grooming?
If you have concerns about the health or welfare of an animal, you should be recommending they see a vet for a consult, discussion about quality of life (QOL), pain relief or whatever else is appropriate. Sometimes people just need somebody else to say it.
Groomers often recommend people bring their pets in for skin, ear or nail infections that they noticed. Saying something like “I noticed Fluffy is not getting around as well lately, have you considered taking her into the vet for pain relief?” might be all the nudge they need.