With Rick, Carl and Morgan all recently departed, Carol and Daryl are The Walking Dead's last two remaining (and surviving) characters from season 1. They've done pretty well for themselves, considering that at this point in the comics, neither of them are around - Carol because she was killed off, and Daryl because he never existed in the first place.
The Walking Dead has a reputation for killing main characters with gleeful abandon, and the majority of people who have appeared in the show - whether in key roles, supporting roles, or small roles - have since been killed off. The original survivor group camped outside Atlanta saw several casualties in season 1, including Jim, Amy, Jacqui, and Carol's husband, Ed. Others proved to be somewhat resilient, with T-Dog, Dale, Shane, Andrea, Lori, Sophia and Merle all making it to season 2 and beyond... only to eventually die off one by one.
Over time, having survived so long, it began to seem like certain members of the original season 1 group were "safe" from The Walking Dead's death curse: Rick and Carl Grimes, who seemed to be protected by Rick's protagonist status, and Carol, Daryl, and Glenn, who were enormously popular characters among fans (with Daryl inspiring the rallying fan cry, "If Daryl dies, we riot"). Glenn's death at the hands of Negan came as a shock, despite being lifted straight from the comics, and left just five of the original characters in the show: Rick, Carl, Carol, Daryl, and the recently-returned Morgan, who was one of the first people Rick met after waking from his coma.
Morgan, of course, has now teamed up with a different team of survivors in Fear the Walking Dead. Carl succumbed to a zombie bite, and Rick is gone from the show for good, presumed dead by his friends (though he's actually going to return in a trilogy of Walking Dead movies). That means that Carol and Daryl are now the last remaining links to the show's origins, and are arguably the most interesting characters purely in terms of how long we've been following their story, and how profoundly the friendship between the two of them has been built up over the years.
Beyond season 1, the pool of characters from the early seasons of the show is also continuing to dwindle, with Maggie leaving Hilltop to team up with Georgie, and Michonne soon to be departing as well. The Walking Dead has been spending more time with newer characters like Magna's group, Carol's adopted son, Henry, and the young spitfire Judith Grimes - presumably in an effort to replace the old guard who have either died or departed.
While Carol and Daryl seem to be safe for now, there's a major event on the way that promises to thin the ranks of The Walking Dead's survivors. The Fair, often compared to Game of Thrones' Red Wedding, is an infamously bloody turning point in the war against the Whisperers in the comics. It seems doubtful that after nine seasons, either of the two remaining original survivors would be killed off in the abrupt and shocking way that characters were killed off in the source material... but The Walking Dead has surprised us before.