uhhh - nope -- protocol soup mix.
FTP has no such concept, (and it wouldn't be part of Apache then either - would it?) Apache isn't really serving that document EXCEPT when a page links to it. Then Apache looks to see if it is configured to serve pdf documents - that's the MIME thing (IF .pdf is a defined mime type and of what type it is.) PDF is an application type. Apache then tells the browser the type of helper that is needed. Webservers can't render .pdf files, so its either find an installed helper app or prompt to save if the helper is not found. Apache only gets requests from browsers or 'things' (applications) that use the HTTP specification to 'act as a browser' (like web-crawlers and content-miners). When you do an FTP interaction with that file, only the FTP server (and the FTP client) are aware of it - not Apache, as there was never an HTTP request.
(Browsers can act as FTP clients - but only when a URL begins with ftp:// -- and that will rely on the presence of an FTP server on the host)
Mime types for Apache are defined in \apache\conf\mime.types
There is a solution, use a script that enumerates the pdf files in the folder and creates links for them. Bingo end of problem. They now can name the files whatever they choose, add or delete them and there will always be a link. You could even include things like the date/time and size.