Are these PDF forms your customers fill out?
You can automate sending the form: upload the blank one to the File Manager and send the link to them in an email from a Campaign or Sequence.
Automating the return of the form is harder. The manual method would be to have them email the form back to you. Then you could upload it into the Filebox in their Contact Record. Your Campaign or Sequence could create a Task to follow up and store the file to remind you this has to be done.
Webmerge would make the return of the form easier, but cannot place it into the Filebox. It would be returned to your email address.
We don't have a way of automating the storage of the file from the customer into the Filebox. There are some Jotform and Wufoo form integrations that store the file on Dropbox and populate a custom field in the Contact Record with the URL to that form.