You did not say which version of Excel is being used.
If it is Excel 2010 and the file was last closed without saving and it has been auto-saved (if set, the default is usually 10 minutes), then it may be possible.
Such files may be retained for a period of time (I think it is 4 days) - they could be found by opening Excel, selecting File | Recent and looking for "Recover Unsaved Workbooks" at the bottom-right of the window.