Unsynced Notebooks in Evernote do not get backed up to the cloud. The notes in your unsynced Notebook stay on your computer hard drive where they remain accessible to your Evernote app on your computer; but, they remain unavailable to your other devices.
You may wonder, "Why would you do this? Why not sync everything?"
From personal experience, I can tell you that not all information is usable in my day to day work. I need not clutter my search results on mobile devices with unnecessary results. If I have to wade through 300 search results every time I am looking for something, it can be irritating.
Therefore, by putting your least used documents in an unsynced Notebook in Evernote, you still have all the wholesome goodness of Evernote without the mobile device clutter.
If you ever need access to a long-term note, you could simply move the note into a synced notebook or make a copy into a synced notebook from your computer. Afterwards, delete the note or move it back into the unsynced Notebook.
The downside to this is that you need to have access to the computer to move documents in and out of cold storage, or have somebody do it for you if you are out.
Another drawback is that without cloud backup, it is your responsibility to do your own backups of your local-only Notebooks on your computer.
One side benefit of using unsynced Notebooks in Evernote is that those notes do not count towards your account note limit, which is 100,000 notes. This is a big limit, I will grant you. But, if you keep that many notes, you could keep growing your stash by taking a chunk of your notes offline.
One last thing to keep in mind is that some of the other features of Evernote do not work if your notes are in an unsynced Notebook, such as sharing. In addition, Evernote requires you to sync images and documents to the cloud in order for their servers to make text within the images and documents searchable.
Keeping offline Notebooks in Evernote does have drawbacks; but, the effects would only apply to notes that you would use regularly. Therefore, the effects on documents you don't intend to use in the foreseeable future are moot.
One good example for using such a system is in a small business or law firm where paperless is the ideal. Your office administrator could maintain your document library on your computer with unsynced Notebooks in Evernote. Projects or cases could temporarily be synced to the cloud for access everywhere. Once the job is done, the notes can be taken offline again on the office computer.
As I write this, I want to point out that long term storage of documents is often confused with having a paperless office, both of which tend to go hand in hand. Going paperless refers to the process of gathering, processing, and sharing of information through an organization. Once the document has done its job, then you need a process for document storage. Your document has performed its duty and needs only stand by in case it needs to be recalled. However, it should not stand in the way of your working documents.
This document life cycle is what I have described for Evernote. Your working documents should remain active and synced across all your devices. Long-term documents, in contrast, can remain locally in an unsynced Notebook just in case you should need them. They can fulfill their obligation out of the way of your working documents.