No, if the government pulls the Dropbox servers (my original stated scenario), your client will not be able to communicate with Dropbox servers, ergo your files will stay intact.
If you mean to say that the government will maliciously delete all files WHILE keeping Dropbox servers online. that is a possible scenario, but extremely unlikely as to not even be worth pondering (i.e. there is no benefit to the government to do that).
Though I must also add: Dropbox is a synchronization service, not a backup service. And even if Dropbox was a backup service, you should have multiple redundant copies of critical files. Don't put all your eggs in one basket and all that.
If you mean to say that the government will maliciously delete all files WHILE keeping Dropbox servers online. that is a possible scenario, but extremely unlikely as to not even be worth pondering (i.e. there is no benefit to the government to do that).
Though I must also add: Dropbox is a synchronization service, not a backup service. And even if Dropbox was a backup service, you should have multiple redundant copies of critical files. Don't put all your eggs in one basket and all that.