When using Microsoft Office 2010 to open an Office document, such as a Word document or Excel workbook, from SharePoint or OneDrive, you may receive unexpected credential prompts followed by the Office application closing with an error.
This is a known issue caused by the following updates for Office 2010:
October 2015 update for Office 2010 (KB3055034)
https://support.microsoft.com/en-us/kb/3055034
November 2015 update for Office 2010 (KB3101521)
https://support.microsoft.com/en-us/kb/3101521
You may also experience an issue with Office 2010 opening SharePoint or OneDrive documents as read-only.
This is also a known issue caused by the following update for Office 2010:
October 2015 update for Office 2010 (KB3054886)
https://support.microsoft.com/en-us/kb/3054886
These issues have been fixed in the following December update for Office 2010:
December 2015 update for Office 2010 (KB3114399)
https://support.microsoft.com/en-us/kb/3114399
You can also use the following workaround: Download the document from SharePoint/OneDrive to your local computer. Open the file to make changes and save it back to the local computer. Then upload the file back to SharePoint/OneDrive.