Following Mavericks upgrade, Microsoft Word closes silently right after opening
I have several Machines which run MS Office 2011 perfectly fine with Mavericks. I would suspect some corrupt settings or cache is the reason for your problem. Try the following:


try moving the Folder "~/Documents/Microsoft-User Data" somewhere else (f.e. the Desktop) and try starting Word
try moving the folder "~/Library/Application Support/Microsoft/Office" somewhere else (f.e. the Desktop) and try starting Word


In both cases the Folder will be recreated with default settings, so if Word starts without problem again you know the source of your problems. If not you can delete the newly created folders and replace them with your previous one.

Please try that and post some feedback. 

Update by asker: removing the above folders didn't help ... but removing ~/Library/Saved Application State/com.microsoft.Word.savedState did.