For a normal fixed-neck guitar, the nut may actually be unglued and you'd never know it until you removed your strings. It's more common than you might think. However, if you're frequently removing and attaching the neck of a guitar as you do with a collapsible guitar - it's not uncommon for the nut to come loose due to the friction and change in pressure against the nut.
This is actually a very quick fix. To repair, simply remove the strings, add cyanoacrylate glue (super glue gel or gorilla glue gel) to the bottom of the nut and put it back in place - be sure to align the nut slots with the slots in the black string retainer. Hold it in place for around 3 minutes or until the glue dries, and restring your guitar - you should be good to go.