If you e.g. had a directory
You have user1 and user2
Create a group editors.
Add user2 to editors..
chown user1:editors /share/documents
chmod u=rwx,g=rx,o-rwx /share/documents
create the document that user2 should be
able to edit but not delete in /share/documents
e.g. as user1
date > /share/documents/some_file
chgrp editors /share/documents/some_file
chmod g=rw /share/documents/some_file