You can download PDFs with restricted access while off-campus through a proxy connection provided by your institution or library.
If your institution or library is not on the list, ask your IT department or librarian for help. If your institution supports remote access via "EZProxy", they can provide you with a proxy URL, e.g. http://ezproxy.example.edu/login?url=$@. Note, the "$@" is a placeholder that tells Paperpile where to put the URL that should be accessed via the proxy server.
If Paperpile can't access a PDF, it will retry downloading it through your proxy connection. You can configure multiple connections and activate and de-activate connections right from the main screen using the proxy connection menu on the top right: