Some obvious examples
- the holodeck gets a fatal software error and people are stuck in a classic novel
- a shuttle breaks down and crashes into a habitable planet
- the federation loses a space battle, but thankfully there's some space jungle (nebula, asteroid field, etc) to hide out in, thankfully within sub light distances
The chief engineer saves the day by inverting the polarity on the matter/anti-matter phase injector system allowing the ship to escape the space anomaly they are trapped in