I've heard that after contracting certain diseases individual immune systems sometimes deem the diseases not worth fighting. Is this true? If so does that mean that there would be no specific antibodies for a disease that your body decided to ignore?

Immune system? It's very complicated and we are learning more day by day. How your immune system recognizes yourself versus foreign tissue is not quickly explained. You don't wan't your immune system to attack everything either. Read about the human biome by an internist at NYU. An overuse of antibiotics can kill off your good "bugs".
No insurance. the antibody response varies depending on the illness. Some directly attack the immune system ( HIV) and certain patients cannot fight off infection or manufacture antibodies ( many/most forms of cancer). Vaccinations often help our bodies form antibodies, but it is not that the body deems these not worth fighting.