Lymphocytes, phagocytes, antibodies and complement work together to defend us against infection. We need this combination and variety of cells and molecules because infectious organisms each pose unique problems.
In rare cases one or more parts of a person's immune system do not work properly. This is called "Immunodeficiency". A defect in just one part can have serious results for the proper working of the system as a whole.
Sometimes the defect is already present when a baby is born. This is because of a fault in their genetic code. These defects are known as "primary immunodeficiencies".
Sometimes defects develop in older people. The are called "secondary" or "acquired immunodeficiencies". They happen because parts of the immune system stop working properly. They can be caused by infections which depress or destroy the immune system. HIV infection causing AIDS is the most extreme example of this. Other causes are cancers and the cell-killing drugs and irradiation that are used to treat them.
Some of the problems that can arise from damage to the system
If your body stops producing neutrophils for any length of time then severe infections are inevitable. At first these are fairly easy to treat with antibiotics, but eventually infections with resistant bacteria and fungi occur.
If you didn't have any IgA antibody you might suffer from more infections than usual.
The helper T-cells of people with HIV infection gradually stop working properly. Because of this they cannot fight infections and develop AIDS (Acquired Immune Deficiency Syndrome).
Very occasionally a child is born unable to make any B or T cells. They become ill very quickly and usually die from infection. Treatment by bone marrow transplant may nowadays sometimes be possible.
Some people have normal numbers of neutrophils but they don't work properly. They generally suffer from repeated abcesses and ulcers which do not heal easily. This is called the "Lazy Leucocyte Syndrome".