Korbit just sent out an email notification to all of their existing customers, myself being one of them, that they wouldn't be supporting Ethereum Classic, a.k.a. ETC because of the vulnerabilities associated with it in relation to the forked version of Ethereum. They said they'd consider supporting ETC, however it appears they're going to continue to watch and see what will happen to other exchanges which have opted to support ETC trading. I recall Korbit not being fast to support Ethereum trading in the early days either until it started getting really popular on exchanges like Kraken, but as it got more mainstream, they added features.
I think it's smart that Korbit is being prudent here to avoid potentially major issues with supporting ETC. Many exchanges are taking a lot of risk for short term profits associated with trading volume on ETC. Many people talk about how its only a matter of time before there's a bit attack on ETC.
It will be interesting to see what the ration of exchanges who support versus those that don't when it comes to ETC.