Yes, depending on your state. Numerous states set a maximum for the amount a landlord can charge as a security deposit (this is based on the monthly rent). For example, the security deposit could be two times the monthly rent. Therefore, if the monthly rent goes up, the landlord could require the tenant to put additional money toward their security deposit. This additional amount would usually be due at the same time the rent increase takes effect. Sometimes, the landlord will not ask for additional security deposit money even as the rent is increased.