"Stealing" in the sense of depriving you access to the documents should be prohibited, but I see no problem if someone requested you immediately copy all of your research.

In fact this is exactly the case with anyone working directly for the federal government, doing research or otherwise. You're told in no uncertain terms that at any moment information on your work laptop can be FOIA'd in which case you will have to immediately hand over the contents of your hard drive (if it has been determined there is a reasonable likelihood that it contains the FOIA'd information). Obviously if you're working on classified state secrets the process is different (also personal information is redacted from the documents). There's no reason research can't be accomplished successfully given the condition that the public has a right to that information at any given moment.