Two solutions :
1) avoid putting the user's name in an Author field
2) use the QuerySave event to remove the name when the document is being saved
In solution 1), you can perfectly well allow a user to create a document without giving that user author access afterwards. Be careful though, because if the user has author access, he will only be able to save it once.
Which means that you will probably get to a scenario where you want the user to be able to save freely until the document is "published", or otherwise declared "finished" by the initial author.
Which brings us to solution 2), in which you check on save what the status of the document is and, if "finished", you remove the author from the field.
Also, note that a document can very well be saved without anything in the Author field(s) at all. In which case, one needs to have at least Editor access to the database to be able to edit it.
Pascal.