The copy of the file that Dropbox stores in your local file folder is NOT the same thing as a local copy. That Dropbox folder is under the control of Dropbox, not you. If you want a local copy of documents, then put that copy in some other folder. Yes, this means that you will have two copies of the document on your hard disk and that may seem redundant but just think, redundancy is the same thing as backup. So be redundant.
In fact it would not be a bad idea to keep many extra copies of an important document like a PhD thesis as it evolves. Either install and use a revision control system, or just save a copy every week with the date added to the filename.
Sorry to hear about the loss. I hope you can get your files back.
EDIT: I've not used Dropbox. I gather from gokce's comment that you did have local copies, but Dropbox deletes them when they are deleted from Dropbox. That's unfortunate.