S.C. Code § 7-11-55
If a party nominee dies, becomes disqualified after his nomination, or resigns his candidacy for a legitimate nonpolitical reason as defined in Section 7-11-50 and was selected through a party primary election, the vacancy must be filled in a special primary election to be conducted as provided in this section. The filing period for this special primary election opens the second Tuesday after the death, disqualification, or approval of the resignation for one week. The special primary election then must be conducted on the second Tuesday immediately following the close of the filing period. A runoff, if necessary, must be held two weeks after the first primary. The nomination must be certified not less than two weeks before the date of the general election. If the nomination is certified two weeks or more before the date of the general election, that office is to be filled at the general election.
If the nomination is certified less than two weeks before the date of the general election, that office must not be filled at the general election but must be filled in a special election to be held on the second Tuesday in the month following the election, provided that the date of the special election to be conducted after the general election may be combined with other necessary elections scheduled to occur within a twenty-eight day period in the manner authorized by Section 7-13-190(D).
The procedures for resigning a candidacy under this section for legitimate nonpolitical reasons are the same as provided in Section 7-11-50.
Where the party nominee was unopposed, each political party registered with the State Election Commission has the privilege of nominating a candidate for the office involved through a special primary election in the same manner and under the same procedures stipulated by this section.
S.C. Code § 7-11-55