Is it possible to be reborn for all eternity?

According to Buddhist teachings, is it possible to continue to reborn and suffer for all eternity? Suppose if a being never attained any merit, never was able to work through its old karma. Would it be possible for that being to never escape suffering? I have heard some people say: > No, nobody can be reborn and suffer forever. For an extremely long time, maybe, but not *forever.* I mean, *forever* is really an astounding concept. Even if you take billions of trillions of gazillions of births it's still *nothing* compared to *forever*. If it's *not* possible to be reborn forever, then it implies that all beings are eventually destined for Enlightenment. Some may have an insanely long way to go, but if they're not gonna be reborn forever, then they have to *eventually* attain Enlightenment? **Do some beings continue to be reborn and suffer forever, or are all beings destined to attain Enlightenment *eventually*?** I prefer answers that give sources and all that. But some nice reasoning is also welcome.