From what I understand, Eckerd was long an arm of J. C. Penny, which was looking to dump the thing for years before it was able to. That notwithstanding, Eckerd went on a building spree in Columbia a few years before the chain was finally taken over by Rite-Aid.
This included building a number of new stores which went under even before the take-over was in the works, and this building, at 1720 Taylor Street (between the train tracks and the old Big-T) was one of them. My memory is that it closed down almost as soon as it opened, though that may be something of an exaggeration. I'm not sure if it was caught in the chain's problems, or just not a viable location. Dollar General proves retail can work in that spot, but Eckerd's was a bit pricier.
UPDATE 15 May 2011: Changed closing date in post title to April 2000 based on commenter Andrew's research.