What the infosec bods should be doing depends on the way the organization runs its IT, what compliance requirements are applicable and how the assets are configured.
A single host will have a footprint much greater than its own filesystem - it will be referenced in monitoring systems, provisioning systems, backup systems, remote access, DNS....failing to ensure the host is remove from these provides a cover for a cuckoo to assume the machines identity (not to mention the operational impact of errors flagging up on these - although that's not the realm of infosec).
There may be accounts configured specifically for accessing the resource, certificates/other encryption keys, firewall rules which should be removed. There may be an allocation of software/hardware licences associated with the device, or even specific licensing files deployed on the device which should be recovered.
Its usually a good idea to retain some capability of restoring the service for a short period after switching off the service, and there may be a requirement for preserving the data for forensic/audit purposes for longer.
In short:
- the security config for the device needs to be backed out of the infrastructure
- assets may need to be recovered
- data may need to preserved