Oscillators shouldn't work
But doesn't it mean that the signal will continue growing until it
  hits one of the supply rails?


Yes, it’s a common problem in some oscillators e.g. the Wien bridge or phase shift oscillator and, the output amplitude can hit rail to rail proportions but then it will stabilise. Quite often you see special add-on circuits to the original “theoretical” circuits that stabilise amplitude and give remarkably good quality sine waves.