An action for damages to a rental premises is an action based in contract (the lease). That means that the statute of  limitations, or time to sue, for a breach of contract applies. In TN, that  statutory period is 6 years--so legally, the landlord or its managing agent may take action against you for damage up to 6 years after the expiration of the  lease. There is no penalty for  waiting--a person or business  may seek damages any time within the statutory period. To prevail, they would have to show that you (or your family, guests, or pets) caused the damage they are seeking to recover compensation for.