Everything old is new again after a few decades in the strength world. They'll fall out of love with it again in a few months, and search the books for another old decent exercise to promote.
These go back to a guy named Angel Spassov. Spassov was a Bulgarian strength coach that came over in 80's, and got in with Joe Weider for a while. His big thing was the combination of split squats and heavy step ups. To help popularize his program, he and Terry Todd wrote some stories on Bulgarian and Russian training where Spassov insinuated that they were moving away from squats to more single leg training. He never outright said they were dropping back squats, front squats, etc...., but he gave you enough to get you thinking in that direction.
Fast fwd a few years, and more Eastern Bloc coaches and lifters are coming over and being asked about this, and the answers ranged from "Nope, we don't know what this is" to "Yeah, we do stuff like that when we're burnt out or as a secondary exercise."
The Bulgarian thing fizzled out back then, and Spassov went on to be a pretty wanted coach in the States -
http://www.overspeedtraining.com/spassov.html .
For what it's worth, the original Spassov Bulgarian Squat only had your back leg a little off the floor like in the below picture -

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