System Updates for deleted files

This may not be exactly what you are looking for, but if you are a System Admin, under Setup --> Recycle Bin, you can see Recently Deleted items (projects, tasks, issues, documents, templates). It will show you who deleted the item and the deletion date/time. The only caveat is that recently deleted items only show on this list for 30 days. So, if item was deleted more than 30 days ago, it would not be on the list.