What do you call it when a system's own output is used for its input?

What do you call the action taking the output of a system (any system: a societal system, a mathematical operation, a recipe) and using it as an input?

I don't necessarily mean when output of a process is always used as its own input, like sourdough production or if a Marmite factory also produced beer. I do not mean that the output is necessarily something that always goes back in; I am meaning that such feedback is possible, neither excluded nor required.

Again, I'm referring to when this action can and does happen. For example: when a university student later teaches at or otherwise works for the same college he graduated from, when a function that takes in functions receives itself, when the fillings that fall from several tacos falling into a tortilla being used as a napkin in order to make one last taco; in general, where a hierarchy points at its own predecessor in a way that logic doesn't break.

I have seen "nepotistic" and "incestuous" used as pejorative metaphors, but these are only metaphors, and are not neutral. I am looking for either a single word or a phrase.

Very generally, a system like this can be described as a feedback system/loop, where the output of the system is fed back as an input to the system. The classic example is audio feedback, which occurs when you hold a microphone near a speaker - minor noises are picked up by the mic and amplified by the speaker, which is then picked up by the mic again, and amplified even more, until you have an ear-splitting ring after a short time.

Your examples seem more focused on productive use of otherwise useless byproducts, though, rather than feeding system output back in as input. You can use the byproduct of beer brewing to produce Marmite, but you don't directly use the product/byproduct of beer brewing to brew more beer, so it's not exactly a feedback loop.