If I understand your question correctly, you are asking for a definition and example of what these warning-type responses are. A warning means that if the person who apologized continues to behave the same (or make the same mistake), you will change the way you act or behave towards that person as a result. For example: If you lent him your car to drive and he gets into an accident and apologizes. That warning response would be that first example "I don’t think that I will lend you anything anymore." Another would be if you were meeting someone for a movie and he/she arrives late and apologizes. You could say: "If you keep showing up late, I just won't go to the movies with you anymore."