Based on your post, I understand that you have never heard of such positions, have not known anyone who has taken such a position, or even inquired of a company of such positions. I gather there is lots of self-selection going on here.
I will speak for my company when I (and my executives) had unpaid interns - the unpaid internships that were with executive management were posted in the career listings of our four main go-to schools which were Harvard, Williams, Amherst, and Princeton. They were slated for only superior rising juniors and seniors. In addition, I had three professors that I used as sort of headhunters that would, after clearance with the career office, present to the top students in their departments, as a special opportunity if they were interested. (I personally got such an offer out-of-the-blue for doing research my sophomore summer, as the researcher called one of my professors and said he was looking for a student to assist with a new thing he was working on. I darn sure jumped at the chance given who the researcher was, and I would be learning and partaking in something completely new at that time, and not done before. I was given a small stipend to cover food, but was never paid a salary of any sort - duration 8 weeks.)
Additionally, we have had top students contact us directly about learning about an area of the business and whether there were short 2 to 4 week unpaid internships available. Yes, those kids could afford not being paid. I personally did two of those myself back in the 80s, as well.
Such listings at colleges still exist today, as my DS found several at his school this past spring - it should not be difficult to have a student search them out, but tell them be very careful about putting them out in public, as I know that the schools protect their listings, even for the paid internships, from public disclosure. Even in the 80s, we were not allowed to distribute the internship information from the career office to people other than other students in the college, as the companies were very specific about which schools and type of students apply.
Outside of the school’s career office, the easiest way is to contact the main trade organization of the industry you are interested in or a specific company directly and ask which executives in which companies / divisions have unpaid shadow internships in X field(s) for you to learn how Y functions.
As for me, my interns never did grunt work, as they were way too smart for that nonsense, needed real thinking stuff to remain engaged and were actually in a learning environment, not a working one. That was not hard to do for they were there to observe and learn the workings of whatever position they were shadowing. It was often tough for many to keep up when they realize how difficult it could be to solve a problem on the other side of the world in 6 hours.