What happens to people with bell's palsy?

Several things. Other than the obvious facial weakness causing cosmetic problems there are other things: 1. Can't close eye - this will dry out the cornea, lead to abrasions and possibly blindness if not treated; 2. Speech difficulty as the lips will be paralyzed and unable to help form sounds; 3. Eating difficulties - along with #2, weak lips will cause food to drip out of the mouth.
Most get better. The vast majority of people with bell's palsy will get better. This may take weeks or months. Some will have some residual weakness and a few will have permanent paralysis.