What can be done to improve the social health of an elderly loved one?

Social groups. If they're physically capable, get him or her involved in social groups for the elderly, many of which you could find in your community through your city/township or the church/synagogue. If they're more debilitated and limited, lots of socialization can be found in an assisted living facility or even a nursing home.
Social health. Check out http://study.com/academy/lesson/what-is-social-health-definition-examples.html. 1st look to family to engaged w/elders. Consider using them as resource to learn about family history. 2nd look to community to find like-minded individuals eg similar hobbies, vocations, interests, etc. Consider volunteering at art & science museums and at schools. Religious institutions can provide options.