After a lease expires and a tenancy becomes month-to-month, can the previous expired lease still be honored in court?

Question Details:

Our tenants went month-to-month after their lease expired. When they moved out, they didn't give a 30-day notice (stated in the previous/expired lease). They also didn't pay the last 2 month's rent. They said that because we didn't have a contract after the lease expired, they weren't obligated to pay us anything. They actually want their security deposit back and are preparing to take us to court. I do have an e-mail where they finally say "OK" to the month-to-month "e-mail" agreement.

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