Here's a buck converter with what looks like an unusual flyback connection:
https://patents.google.com/patent/US3959716A/en?oq=7782002Probably they opted for this, to get a common [AC] ground for the switch -- easier to drive, no bootstrap, and less level shifting needed. Switching supplies were new back then, transformers were cheaper than transistors (well, maybe not quite
that cheap), and so they weren't afraid of using coupled inductors. We tend to avoid coupled inductors nowadays, just because of commercial availability, really.
Analysis:
We can guess the phasing of the coupled inductor (who needs to read the text?). If the diode conducts while the switch is on, that would be bad (large peak currents). Also, if it were phased so that this happened, it would only conduct if Vin > 2Vo (assuming a 1:1 turns ratio), which is weird and useless.
We conclude they are phased the same direction (dot on the same side). The diode is then doing catch (flyback) duty. The inductor voltages during turn-on, off and idle can be written out assuming one or the other (switch or diode) is shorted, or both open.

If we swap the switch to the Vin side, and the diode to the GND side, we find it's essentially a centertapped inductor, except it's not a center tap at all but a double end tap -- in other words, a short circuit. (Actually a common mode choke, but not a very useful one as one end is shorted.) We can remove one winding, shorting nodes A and B together, and we find we have an ordinary buck topology.
I hope this analysis has been educational. Any other oddball-but-not examples?
Ooh, flyback transformers are a good one, come to think of it. Anyone want to do the "B+ Boost" from ye olde television?

Tim