Since you're identifying the terminally ill as a prototype group it might be best to investigate hospice programs. My experience as a caregiver was enhanced by a hospice social worker who not only counseled the patient, but also the primary caregiver.
I like the idea of discovery and curiosity to find social, historical or occupational links with people. Modeled after geocaching, maybe individuals could add a cache...storytelling about a person in that place. For example, children could write a cache biography about their parents or grandparents' experiences.
I think it would be great if the existing companies could offer this service. Maybe caregivers could get a "discount code" from a nonprofit that would oversee the usage. Analogous organizations like McDonald house that provide lodging for families of inpatients could be a model.