By your interactions with them. Sure, after-the-fact caring won't result in any external effects, but a lot of caring is expressed in interaction which is indeed left with people. Who in turn have other cares and interactions influenced by those who cared about them. It's a chain.
If you care about that little red-headed girl you knew as a nearly-bald kid, and you die in a cabin in the woods, how is your care passed on?