Is data from iCloud files stored locally?

I have a strange problem - while uploading some documents to iCloud, my computer unfortunately crashed and I don't think it completed the process (it was an old MacBook Air 2011 running Sierra so I knew it was on it's last legs but that was a stroke of bad luck). Turns out there were damages to the hard drive and it is unable to recover. I got the data extracted and I'm shifting through the files to find the documents I'm looking for. I'm wondering if and where data from iCloud files are stored locally and if there is a way to extract them.

Thank you :)