way of escape; escape route
Refers to a physical or metaphorical means of fleeing or avoiding a situation. Often used in contexts of planning an exit or finding a loophole.
Check the escape route in case of fire.
He always has an escape route ready in the form of an excuse.
Compound of 逃げ (nige, 'escape') + 口 (kuchi, 'mouth, opening'). The exact historical derivation is uncertain, but the word literally suggests an 'escape opening'.