Effective policies and standard conventions are always beneficial for an organization.  They are especially required for difficult tasks like employee terminations where emotions may supercede good judgment.  Companies should protect themselves defensively in these situations. In doing so, they also protect the employee from potential liability. 

Best Practices – Corporate Termination Policies

QUOTE: It is important to have a policy for limiting access to corporate technical resources after an employee has been terminated. Some basic step include: disabling user account(s), changing or locking all the passwords the former employee had access to, disabling corporate e-mail access and locking down access to their personal workstation.

An email from HR using a pre-configured template to all key stakeholders with a mean of reporting back to HR, confirming the work has been completed, would help prevent this kind of malicious activity. Of course, the account(s) should be monitored to detect potential unauthorized access.