Your elderly relative is a piece of shit. Put him outside.
Edit: Also, take the cat to a vet and start thinking about end of life care for this sweet kitty and whether you want to lift a finger for your relative once he's in a similar position.
There is value to having the conversation about "holding on for too long". But...
But, "euthanasia vs palliative care" is a conversation that must be between you (the owner) and your vet
It's possible that there are other, addressable reasons for being unable to make it to the litter box, and a vet visit is necessary to identify and address these issues
As well, it's possible that it is indeed "time". A conversation with the vet is best