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No, they cannot. With no lease, your tenants are month to month tenants. The following SC statute requires at least a 30 day written notice.
South Carolina Code 27-40-770. Periodic tenancy; holdover remedies
(b) The landlord or the tenant may terminate a month-to-month tenancy by a written notice given to the other at least thirty days before the termination date specified in the notice.
So, you are entitled to rent for that 30 day period for which no notice was given and you are entitled to recover damages. The deposit covers both unpaid rent and damages and if it is not sufficient to cover both, you are entitled to recover the shortfall. So, you do have recourse against them for these amounts. If they won't pay you voluntarily, file suit against them. Filing the suit will give you the collection options and leverage you need to collect the debt owed you. That's because once the suit is filed and a judgment awarded, you become a judgment creditor, and if they don't then pay the judgment, you can have the sheriff serve a summons on them for a debtor examination. That forces them to meet you in court again and answer questions under oath about their assets. After that information is obtained, you have the power to attach bank accounts, have the sheriff seize other personal property, and/or place liens on any non-homestead property they own to satisfy the judgment. In my experience, simply filing the suit is typically all you need to do to resolve this outside of court because most of the time, once served with a summons they are being sued, they will pay you rather than spend the time and money defending a suit they cannot win.
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