I am actually doing this for science extra credit. My teacher said that we would die if the moon got too far away. He wants us to figure out when this will happen.
The moon will not ever leave the earth's orbit entirely. Eventually it would reach a distance (and the earth's rotation would slow) so that the earth always kept the same face towards the moon. After that it would recede no further. But the sun will become a red giant, probably engulfing the earth, before that happens.
The moon will never spiral away. In case you did not know, the moon is moving away from Earth a tiny bit each year due to tidal effects and when Earth always has one side facing the moon, the moon will stop moving away. When they are tidally locked (always have one side facing each other) the will rotate at nearly the same speed.