The Southern Conference was once the home of many of the SEC and ACC programs but today its a highly respected FCS conference with schools in primarily in the Carolinas but with one member in the states of Tennessee, Georgia, and Alabama. It is home to 11 members as a result of the announced departure of College of Charleston. It's a mix of public and private institutions and 2 (previously 3) members do not play football in the league:
Private schools are in Blue
The SoCon is a league that is going to lose members--FCS football superpowers Georgia Southern and Appalachian St are leading candidates for the FBS Sunbelt Conference. The CAA, if it can hold together, has been looking at Davidson with longing eyes for a long time and they would be willing to admit another Carolina school like UNC Greensboro or Elon to accommodate them. The A-10 might also be interested in the Wildcats. If this league were to take heavy hits it could cause UT Chattanooga to petition the Ohio Valley Conference for admission as the two schools would fit into their footprint.
As far as schools that could join the SoCon, East Tennessee St would like to re-enter the league after being exiled to the OVC after dropping football. OVC member Jacksonville St might also have an interest in the league. I would consider every Big South school as having an interest in the SoCon with the football playing members being the most likely to be included. The members of the Atlantic Sun Conference would probably like to be in this league too but their chances are much slimmer with maybe the exception of Georgia schools Mercer and Kennesaw St.