Nice question Brittany,

The answer depends upon how long the cycle stops for. We know what happens in a way since this has happened at least 3 times and possibly more in our recorded rerords. The most famous of these is known as the Maunder minimum where there were no sunspots detected on the Sun for about 70 years (1645 - 1715), i.e. there was no sign of a solar cycle for ~7 cycle periods. This period coincided with more severe and longer winters in northern Europe and north America: known as the Little Ice Age. So an extended suppression of the soalr cycle can cause some severe changes in the weather patterns on the Earth. The Sun "recovered" from this period to restart the cycle again. How this happens is still a mystery.

Cheers - David