I think it depends, in part, on two factors:
1. Is there a policy regarding the disposition of communications (email/letters/etc)?
2. Is there an active investigation or legal action which may be impacted by the destruction of such communications?
There may be other factors. If there is a policy on how to handle such correspondence (that was not suddenly implemented in response to potential inquiries), that can be a protection against any sanctions. Those policies are overridden by legal actions, like a subpoena, which may demand that any documents or evidence related to a case or investigation must not be destroyed.
Edit: As no-zombie pointed out below, destroying evidence of a crime would supersede any of the above considerations.