if there is no lease agreement then there's no argument on there part as having a right to stay there.
If there is no written lease, then there is what is called a month to month tenancy. Most states have statutes that govern the responsibilities of a tenant and landlord in such cases since there is no written lease. A tenant lives there indefinitely as long as the tenant pays the rent monthly, does nothing destructive or the landlord gives the tenant a Notice to Quit the Premises and Deliver Possession of the premises by a certain date. If a tenant fails to pay the rent or does something the statute forbids, the landlord goes to the landlord-tenant court for an eviction in the same way as if there were a written lease.