Yes, in South Carolina, the parents could be arrested for contributing to the delinquency of a minor. By allowing minors to drink in their house, even though they didn't supply the alcohol, the parents are aiding the minors by giving them a place to drink. Because possession and consumption of alcohol by someone under the age of 21is illegal, the parents are aiding the minors in breaking the law. Contributing to the delinquency of a minor is a misdemeanor and if convicted, the parents would face a fine up to $3,000, up to 3 years imprisonment, or both. SC Code 16-17-490.

In addition to any criminal liability, the parents would also be subject to civil liability. This is called social host liability and it means that the parents could be sued for any damages that arise due to the people drinking at their house. For example: if one of the minors drinking at the parents' house leaves the party and gets involved in a car accident, the minor who was drinking, and the people in the car he hit can sue the parents.