Some users may create a new Contract Status picklist value to illustrate that a Contract has been terminated. However, it should be noted that Contracts can not be "Deactivated". Though the Status picklist field might show a value indicating that the Contract is no longer active, it will still be considered Activated by Salesforce CRM.
If the "Send Contract expiration notice emails to Account and Contract owners" option is selected in the Contract Settings, an email will be sent to the Contract owner regarding the impending expiration of said Contract. This can cause confusion for users, as they will not be expecting an Expiration Notice from a "canceled" Contract.
To prevent an Expiration Notice from being sent, a user must manually set the "Owner Expiration Notice" period to "--None--". Furthermore, since it is impossible to set a Field Dependency for the "Owner Expiration Notice", Data Validation rules must be employed to force users to set the period to "--None--".
As an example, if "Terminated" is added as a Status picklist value, the following Validation Rule would require disabling the "Owner Expiration Notice":
ISPICKVAL( Status , "Terminated"),
Alternatively, if the Org can use Workflow Rules, create a new Rule based on the Contract Status Field. The Immediate Workflow Action would set the Contract Expiration Notice to --None--.