The permanent markers ink is specially designed to penetrate the cell walls of plants or cellulose, which is effectively used when dying paper or fabrics.
Nail polish remover is made up mostly of acetone, which is a very strong solvent that can remove all kinds of stains from your clothes or other fabrics, including sharpie and paint stains.
Vinegar is a product that we all have in our homes, and because of its natural acidity, it is a perfect product to use for removing permanent marker stains from your clothes.
Try using materials that everyone has in the house. For example, mix a solution of dishwashing liquid, vinegar, and some water, and use it on the stain.
Like any other surface that you find with sharpie marker stains, the key to success is removing the stains as quickly as possible and not leaving the stain for too long.