I think "getting eaten by vultures" is (from our vantage point at least) pretty much the same as "going away by themselves if left alone". That is, it's not like you need to spend money or resources to deal with the problem, you just let nature take its course.
All you need to do is not poison 99% of your vulture population, which is what India did. They learned their lesson, and based on your Wikipedia link, the poison is now banned and populations are starting to recover.
“ The opposite of a civilization in this context, where people neglect the elderly and let them be eaten by vultures without care or concern, could be described as barbarism or a dystopia. These terms often carry connotations of societal decay, where moral and cultural norms have broken down, and the community fails to uphold basic human dignity. “
That’s too simplistic. The situation depends on multiple parameters, including rate of children (future workers) being added, rate of automation advancement, energy supplies, and changes in length of non productive years due to technological advances.
It is obviously possible for old people to live too long so as to become a net cost to society, which means the resources used to keep them alive take from resources that could be spent elsewhere (such as on the young). In fact, that is the top political problem in almost all modern democracies, even though it is not stated that plainly.
All you need to do is not poison 99% of your vulture population, which is what India did. They learned their lesson, and based on your Wikipedia link, the poison is now banned and populations are starting to recover.