When you turn on the backup function in OmniOutliner's general preferences, a backup version of your outline is kept in the same folder as your primary outline. In the case of a crash, power failure, or other nasty event, the backup version will remain in the folder as "[file name] (Autosaved).oo3". When you open your document again, all backup copies will automatically reload.

If the backup function is turned on, an indicator may briefly appear in the center of your document to indicate that the file is being backed up.