You'll a Plug in that offers more options for handling files than are possible with straight filemaker. The moo plug (you can google this), on option. It's free, but windows only. There are other plug ins offered by other third party developers.
With one of those plug ins, you can generate a list of files in a given folder. You can then use a script trigger to pull up this list and compare it to the list stored in your database to update it so that links to new files appear and links to deleted files disappear automatically.