Soluble fiber is broken down partially in the gut by bacteria/fermentation. Lots remains. Insoluble fiber passes through mostly unchanged.
You see where this is going.
You need only minimal new inputs and the rest can be recycled.
To extend D Rumsfeld
there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns—the ones we don't know we don't know.
And now things that we know and wish that we didn’t (ie spaceship recycling)
Pee is largely recycled right now on the ISS. It's mostly water.
And nitrogen is good for growing plants - the cellulose of their structure is the ideal insoluble fibre for us. Though, cows turn it into usable sugars.
I heard someone call the ISS closed water system the infinite coffee machine. Yesterday’s coffee becomes today’s coffee.
It sounds gross but if we get good enough at it it’ll work.
Like any settlement on a frontier the first people in space aren’t going to eat well. They’ll survive. After a long time I imagine we will get good at growing and manufacturing food up there. It’s honestly not even close to the hardest problem. Full recycling and modular manufacturing for complex items is a lot harder.