If you are syncing your library in Dropbox, you may have noticed that your original files have very long non-human readable names, or you may not be able to find them at all. Papers 3 needs to give your PDFs these names so that it does not lose them during syncing. If you move, or rename these files Papers will no longer be able to find them. If you need access to your PDFs please use the virtual file system.
In Papers2 you have the option of organising your files with customisable file names, and you can still have this in Papers 3! In order to get back this control over your file names you will need to use the Virtual File System. This will mount a virtual drive on your mac and show you your entire PDF library organised into your own custom subdirectories and with your custom file names, just like Papers 2. It will serve you real pdf files which you can save, email, print etc.
On a mac there's a couple of ways to get to the virtual file system. The easiest way is to double tap ctrl to bring up the Citations window, then click on the small down facing arrow on the right of the search box and choose "browse library in Finder".
Or you can open Papers and go to the Library and click "Open in Finder".