system
Given the following post, respond as if you're commenting on Reddit:
human
[Wall-E] How was the Axiom self-sustaining?

What was originally intended to be a voyage lasting a few years at the most, turned into one lasting 700 years. For the entire time the Axiom has continued to provide for the entire human population aboard. They're kept (very well) fed, they're provided a hover-chair, clothing, etc. 

They're clearly going through a ton of food. They're also many robots aboard that are regularly maintained and need to be repaired with new parts. There are also things things like paper and such that gets thrown away. There's rocket fuel for voyages to Earth to drop off the EVE robots and many other things. When we see the garbage disposal area of the ship we see there is a huge amount of waste being generated. All of which is stuff that most likely will have to be replaced somehow. 

And how does the economy of the ship work? The people aboard seem to live a life of luxury, preforming no actual work of any kind. When the captain does his morning announcements on their 700th anniversary he mentions to ask for a free cupcake in a cup. This being free implies that not everything is free, meaning people have to pay for stuff aboard the ship. Where do people get the money for things? The only one who seems to have anything resembling a job is the captain. Are they given an allowance?
gpt
Heavy duty recycling programs, external matter scoops to recoup fuel (likely hydrogen and helium) and possible other elements which can be synthesized into food and the like. Onboard refineries and machineshops to produce the materials required for maintaining the ship and it's robots. Automated hydroponics and cell-cultures sustained by recycled waste and collected hydrocarbons. In principle, creating a self sustaining generation-craft is doable (and most of the systems to allow that would also be necessary for a mission lasting several years and sustaining a crew of thousands) and they seem to have most of the technology they would need.

As for the economy... Either they are afforded stipends from the 'Company' which they then pay back into the system for services, creating a closed circuit finance system with zero loss or gain... Or they've become so dense through over-pampering that the term 'Free' has become more of an attraction than actually meaning 'No Cost'.