Church of the Trinity has a somewhat unique pastoral care system which was established 25 years (or so) ago. It involves everyone who wants to be involved and has been an effective way of getting to know one another and sharing news and concerns.
Essentially, everyone who opts in has a “carer” who is another member of the congregation. The relationship is established by mutual agreement through an intermediary who asks both “carer” and “caree” if they would like this person to be their carer / if they would like to be this person’s carer.
This document spells things out in more depth: Caring for One Another – 2006