Can children continue traveling on their foreign passport and permanent resident card, even after their parent has become a naturalized U.S. citizen (N-400)?

It seems that children will also become U.S. citizens when their parent becomes naturalized, so it is not clear if they would be allowed (as U.S. citizens) to keep entering the U.S. on foreign passports. But on the other hand, the children might not have applied for U.S. passports and perhaps never want to.