If the application crashed, then it would still be possible to recover it at /Users/ username/Library/Application Support/ Microsoft/Office/Office 2011 AutoRecovery.
However, if you close a file and click Don't Save, the file is deleted from the AutoRecovery folder.
You can:
Look in your trash for a "Recovered items" folder.
In Finder, select Go > Go to folder, type
/private/var/foldersand look for files named "Word Work File" inside a "Temporary items" folder. Drag the files or folders to the Desktop (or anywhere else) before dropping them on Word's icon. MAKE A COPY FIRST!
However, the chances of finding anything useful are remote, as the document would never have made it from RAM to your hard disk. (Though some users seem to have had some success with the second method)
Final Method: (from the link above)
Go to Finder and open the HD icon in your desktop
Press Command F (for Find)
Next to Search, select This Mac
Click on the first dropdown menu and select Last modified date
Click on the second dropdown menu and select within last
Click on the blank field and type 1 (the search operation will start at this point) Make sure the third dropdown menu says Days
In the main menu bar, select View > Show view options and enable Date Modified
In the search results window, click on the title Date Modified to sort files by date
Read through the list to identify your file. If a likely candidate is found, Option Drag it to the Desktop (this will copy the file, making sure you don't move any required files out of where they might be needed), then try to open it by dropping it on Word's icon.
If you do find one or more file that contain part of the text that are looking for, but also a lot of garbage, try to clean it up as follows (you will still get a lot of garbage and no format at all):
In Word, select File > Open
In the dropdown menu, select Recover text from any file
Locate the file on the Desktop and open it.