Immortality -- if it were like the movies (a state of perpetual whatever-age-one-is-when-attaining-it) would be grand, if it were real, for the youthful and healthy. But for the aged and infirm? It may be another story.
And if immortality meant one would simply not die, and continue to live in perpetuity, then one may continue to age.
I have had many aging friends who welcomed their ends after many years on this earth. I am not saying they wanted to die, but I have known those who were ready to accept death.
Losing a loved one is not easy. However, we are all temporary in this world, and nothing can change that fact.