Or is the only option to delete 'old' computers manually?
So when you are referencing "unassigned computers" that implies that the group to which you are referring is a WSUS Target Group. If my assumption is correct - that you want to know how to clean up the old machines out of WSUS - Microsoft provides a tool that can handle that called the Server Cleanup Wizard.
One of the options in that tool will remove "client computers that have not contacted the server in thirty days or more" (although that time frame could be modified). So it isn't really that it checks Active Directory itself, but it can get rid of 'old' machines from being listed in WSUS.
Traditionally, you'd need to manually run that tool periodically. Patch Manager doesn't change the functionality of that tool at all, but it does allow you to schedule a task to run the Server Cleanup Wizard periodically. In Patch Manager if you select your WSUS server on the left and the right-click that WSUS server name, near the bottom of the right-click menu you should see the option for the Server Cleanup Wizard task.
Thank you kellytice!
That is the exact option that I was looking for. I've used this feature in the past to cleanup old updates and didn't even think to look into it for this issue.