it's that simple. If a system does not report up an inventory within x days, it is considered inactive. Inventory is generally sent daily the first time a client can connect to a server after 24 hrs since the last check-in. If this doesn't happen for 30 days, many companies will delete, or mark as retired, all those machines. If, in the odd chance, one of those is from someone that took a 3 month leave, when they check back in, the computer will be re-added to the database, or can be taken out of retirement. The only draw-back is that if it was deleted before, you have lost the inventory history and can't tell if the customer who was gone for 2 months also stole RAM...
A system is "Active" when it is actively being managed by Notification Server and it's policies. A system is "Retired" for asset retirement purposes. That is, literally, that you're pulling it out of active use because, as an asset, you're retiring it - you've now written off the value of the system and it will no longer be used. Some companies must keep records of all systems they've ever owned, so the "delete" option is not really an option. For those, when a system is unplugged and buried either in a junk heap, closet, or a school as a hand-me-down, then it is "retired" in the Notification Server. It is no longer a "managed" system, which in the DB literally means that a field is changed from a 1 to a 0.
Again, "inactive" means "silent" for that period of time. Why is not what we're concerned about. Could be hung for a month, unplugged accidentally, blown up by a stick of dynamite, agent removed by some hack of an end-user - whatever.
Does that help? A LOT of customers simply use that report. If you've not found it already, you can search for it, or one of us will point it out.