You must turn on this feature. It is not on by default.
If you do something regretable in Beyond Compare, how can you get your old files back?
In TextCompare, there is undo: Ctl-Z
In FolderSync there is NOT an undo. You have to enable "BackupFilesBeforeCopy" or "BackupFilesBeforeSave". These settings are in Tools->Options->Backups
When those are turned on you will start to see lots of files accumulate that have a .bak suffix. (You can set this suffix to other options at Tools->Options->Backups.) Here is a folder with a file and its backup file: