Well, they are no longer the same person they were throughout their life, whether at 60 years, 70 years, or 80 years. Why, all of a sudden, with dementia, are they no longer the same person? It's true that it's no longer the same person because they no longer have the brain they used to have when they lived and related with other people.
We also regularly make decisions through other people for those with brain damage, who have suffered cranial trauma, massive strokes, and so on. We make decisions for them, because they are no longer there to tell us what they want or don't want. We make decisions for them because they have left advance directives with respect to aggressive therapy.
In medicine, it's a fairly regular occurrence for us to make a decision for the patient with the family, friends, etc. We generally do so for cases of aggressive therapy, but then we are no longer dealing with the same person.