In SC, one can draw benefits if fired or quit, but will be disqualified for six weeks before benefits can be received, but you still can submit a claim for unemployment, it just takes a little longer to receive payments.
Can I Collect Unemployment Benefits After Being Fired Upon Return From Medical Leave?
It would depend on your state's laws and the circumstances around the reasoning for your termination. The best thing to do is get the claim going as soon as you can and while at the employment office talk to one of the counselors there.