Disclaimer: The materials provided below are informational and should not be relied upon as legal advice.
Once the lease expires, if you allow the tenants to stay and pay rent, that will make them period tenants (if they were paying rent once a month under the lease, they become month-to-month tenants). For a month-to-month tenant, either side can give 30 days' notice to terminate the tenancy. If you are really concerned about this, I suppose you can sign a two-week lease with them. Be sure to consult your own attorney to protect your legal rights.