What damage is caused when the oil pump fails?

Please explain more what your statement means. What has to be replaced or fixed? What problems can be caused later from this oil pump failure?

On Sunday (20th) my husband drove the car 3 blocks to get the paper. On the way home, he heard a claking sound and then it sounded like marlbles rolling around in a tin can. By that time he was home and in driveway and the oil light came on. He backed it out of short driveway to flat part in front of the house. He waited awhile then checked the oil and it was ok . He started it again and oil light came on again. He checked our manual and it said to call road side assistance and have car taken to dealership. On Monday service dept. called to asked the problem and my husband told them the story. They called about 3:00 to say they were keeping it for next day. On Tuesday about 2:00 and they said the oil pump failed and they had to get parts to repair the pump and other parts and would keep it until the following Tuesday. So the car was not driven without oil except to get it on the flatbed towtruck and to back it out of our driveway. This was a new 2010 Hyundai Sante Fe with 6000 miles on it. We even had to ask about getting a rental from the dealership since the service department did not mention it. And that was a fight to get another SUV since they only wanted to pay for a compact car which I refused since I have very few times driven or ridden in a compact car in 40 years.