I don't have that folder.
I did some googling for cali_core4 and it does seem that it contains calibre code and DLLs. I didn't try to work out why, but I don't think it is reformat. It looks more like some other packaging of calibre.
The site
https://www.advanceduninstaller.com/...pplication.htm contains instructions on how to uninstall calibre 4.6.0. The equivalent instructions for other calibre releases do not mention cali_core4.
My guess is you can delete it.