To make a rough categorization, elderly people can belong to one of two categories: people who have been weighed down by life and people who haven't.
The people who developed the habit to get back up when life pushed them down at this stage in life exhibit a kind of spiritual fulfillment and sense of wisdom we usually attribute to the elderly. For them feelings of stress are temporary and without substance because they are able to look at it from a wider perspective.
The people who got weighed down by life and stayed down have a much more difficult time dealing with stresses at this age. Whatever stresses they had in their adult, teenage and even childhood stages of their life come back and chip away at their personalities. Finding balance at such age is much more difficult, and unfortunately many people just do their best to endure until death comes as a salvation.
The solution to overcoming elderly stress (and also the generally accompanying anxiety and fear) is acceptance - it is never too late to accept, love and recreate yourself.