In previous versions of the Maya UI (before version 2011), as well as the "Classic" OS Native UI that is still available in Maya 2011, if you want to overwrite an existing file, the Overwrite dialog box appears. If you select Yes, and then cancel the export in the FBX exporter window that appears, the FBX file that was to be overwritten is instead deleted.

This is not a problem if you use the Maya 2011 default UI while exporting to FBX because the file browser and exporter options now appear in the same window. If you use the Maya Default UI to export to FBX, you can cancel the export operation without deleting the original FBX file. See Switching the FBX UI.