When file sharing is turned on, or a file server is running, an invisible folder is created on the server called the Network Trash Folder. When a client logs into the server and deletes a file from the server, a folder is created inside the network trash folder (called Trash #1). Any subsequent user who deletes a file from the server, will cause a new file to be created (called Trash #2), and so on. There can be any amount of these folders depending on how many logged in users have items in the trash from the server.
When the user empties the trash on the client machine, the folder is deleted and those items will no longer remain on the server. In the AppleShare Admin program, the administrator has the option to empty the network trash. This option exists because any user who trashes something on the server, then crashes before trash is emptied, will cause those deleted items to be persistent in the network trash folder.
Once the session is terminated, that user has no control over any item that was left in the trash. The administrator can clear out any of these persistent trashed items by emptying the network trash. If a user has trashed a file from the server and logs off from the server gracefully, the finder will put up a dialog saying that all items in the network trash will be deleted.