Your company should really have a policy in place to remove these accounts or at least audit their use.

We have a procedure for removing accounts when someone leaves the company. The account is locked within Active Directory and after 3 months is deleted. The 3 months is to allow any of the remaining staff to request access to the information held in the account.

Different procedures need to be in place when dealing with IT Admin staff who are leaving and especially when being dismissed.

We also have alias accounts for units/departments things like 'accounts@'. We monitor those for use and if they don't seem to be getting used we go to the party that requested it and see if they still need it and remove it if they don't. That's slightly different though in that it's an active but dormant account.