Even in my childhood I had remnants of this. My uncles or not-grandma grandma neighbors could be trusted to take care of my when my mom or grandparents weren't around. Nowadays that dynamic is spending $30+ on a credible babysitter. Those are the sort of dynamics that have recently weathered away.
>I doubt even the children would have gone out of their way to devote their lives to the care of the elderly or the disable
1. Yes they did and do. Many people still love their parents and want to make sure they are taken care for.
2. It isn't really that deep for neighbors. It's just a matter of checking up in them every few days. It isn't full time care. Of course if they get hurt they can either help out in minor cases or call emergency if it's more than minor.
These days you may sadly accept dying alone and not being discovered for weeks if people don't regularly contact you. What does that say about modern society?