There is such a thing as a non-disclosure agreement (NDA) that you could have the person sign (whether they would agree to sign it is another matter, but if they don't and you think your research is something that is worth stealing, don't show it to them if they won't sign). It would be best to see an attorney about this, but if you cannot afford an attorney, I think there are plenty of do-it-yourself NDAs online.
Also, taking another person with you who at least half-way understands the conversation would be good so that you would have a witness to the discussion. That would automatically discourage most people from stealing your ideas.
If they would agree to allow the meeting to be voice-recorded or video-recorded, that would also discourage them from stealing from you, and that would be even better proof in court in case they did steal the idea from you; be sure to state the date of the recording and state the names of the people in the beginning, and state that they are all aware that they are being recorded.
By the way, if the research that was previously stolen from your friend was documented and they can prove the date of when they developed that research (they might have saved it on DropBox or other cloud storage on a certain date, or something like that), they might be able to sue that professor for stealing their work. Again, they should see an attorney about that.
Many attorneys are willing to talk to potential clients one time for free. Your school might even have an in-house counsel who might be willing to talk to you or your friend about these matters for free; however, if the professor who stole the work is from the same university, then talking to the university counsel would be a very bad idea because their first priority is to protect the university and its employees.
The person who said that you should talk to your advisor is on the right track, although your advisor could possibly steal from you also. This all kind of depends on how valuable your research is.
It would always be a good idea to ask if it's ok to do a voice recording at all meetings. I think most people would agree to that. You can also probably get away with taking a photo of any work you write on the blackboard or whiteboard. Always save your research on DropBox or someplace like that at various intervals (do NOT erase old research files, just add new dates to the new research or put them in folders that have the date on them--don't make changes that can change the modify-date to the current date after you save older research). Then you have a way of proving that these ideas are yours and you can show how they changed at various intervals and can prove that you had a certain idea at least by the date on the file. In the past, many people would send plans of things they planned to copyright to themselves in a postmarked sealed envelope and left the envelope sealed in the filing cabinet in case there was ever a question of ownership of the idea.