I used to work for an origami company, but they folded.
Why this joke works
The Company Does What Its Product Requires
When a business folds, it closes down. Folding paper is also the central action in origami. The speaker’s former employment makes the first meaning sound like a straightforward explanation of why the job ended. The industry then pulls the same verb back toward a physical crease. Nothing unusual has to happen to an actual company building; the amusement comes from describing business failure with the very action that would normally make an origami project succeed.
A closer look
The Word “But” Sets Up a Small Reversal
“I used to work” prepares the listener for a reason the employment ended. The joining word “but” promises a setback, and the final clause supplies it with almost no elaboration. Keep the opening conversational and the ending short. Adding a paper-crane demonstration can distract from the contrast between successful craftwork and an unsuccessful business.
Fact behind the joke
Folding Also Solves a Spacecraft Packing Problem
The Smithsonian Astrophysical Observatory’s Origami Universe resource connects paper-folding ideas with deployable spacecraft structures. The James Webb Space Telescope’s large sunshield had to be folded to fit inside its launch rocket and opened after launch. A structure can therefore be useful precisely because it changes between a compact stored shape and a much larger working shape.