The tires can get damaged or completely blow off the wheel depending the how bad the impact of the curb is. When a car curb hops a lot of the force goes onto the side of the tire. However, the damage from a curb hop varies depending on the size of the tires and where exactly it collides.
A tire's strongest point is its tread. When a car curb hops most of the damage occurs to the side of it which generally involves blowing a hole through the sidewalls. Some cases can result in the tire's bead being pushed off the wheel.
The larger the tire, the less likely it will have any damage. Larger tires are made to transverse over large obstacles and the treads or sidewalls are reinforced to handle impacts, such as curb hops.