If you want to write factually, you'd say, "When there is a power cut, the elevator stops working". In safety instructions, it might be written, "In the event of power failure, the elevator will automatically come to a stop". I hope this helps. Emma - Talk2Me English

It's already pretty natural. An elevator stops working when there's no electricity. 'Elevators don't work without electricity' would be slightly better, I suppose. Or, do you want a sentence that you would say if the elevator isn't working? In that case, you might say "The power's out, so we can't take the elevator," for example.