They definitely can and do stop. There are plenty of videos of accidents avoided because of stopping, and this is a rather common feature on most mid to high-end cars now, commonly called a collision avoidance system and grouped under the umbrella of pre-crash safety systems.

The avoidance feature is designed to stop the car in the event of an unavoidable obstacle directly ahead. It doesn't guarantee a stop but it will still apply the brakes faster and more fully than a human can react and thus shed more speed from the impact. Pre-crash safety will also tighten the seatbelts, move seat positions, close windows, and inflate auxiliary airbags in preparation, and these are all well-tested and proven features.