Well, I don't know of any protein folding examples, but it seems a lot like an "autocatalytic cycle" which is an interesting part of origin-of-life theories.
Stuart Kauffman wrote some things about this, but here is a counterpoint from Leslie E Orgel:
Makes logical sense that it would be a part of life (once you can synthesize a few things from a given one thing you can build all sorts of logical structures...), but I see there are tons of biological probabilities at play that I don't understand.
How did school manage to make biology so boring? They did it with math too, so I shouldn't be surprised, but damn.
Would love resources on an intro to bio for the CS folk. I'm sure there are some good ones out there.