How can I keep the files uploaded by filefield module even though users delete them on node edit form?
I used a module called Filefield Sources together with IMCE. And on the file field's configuration page, I enabled the "IMCE Browser" option for additional sources.

I did a few tests and any files attached to a node using the "IMCE Browser" method doesn't get deleted when the file is removed from a node on node edit screen. But files added through the normal "Upload" method do get deleted, so I think you should upload files using the IMCE Browser too as it has a file uploader as well.

I'm not sure how to remove or hide the actual default "Upload" method on the file field though.