What will happen when a person in unable to present antigens to cytotoxic t cells?

The lesion progresse: For a foreign invading cell to be destroyed it has to present the antigen to the T cell system. This mainly hold true for bacteria and viruses presenting the cellular antigen at the Threshold level. Tumors have such a low level of immunogen that they are not recognized.and continue to grow. When antigen is delivered at proper levels as vaccines, it is the B cells that help control the tumor.

Depends: This depends on the antigen. For example, natural killer cells (NK) act as "innate" or native destroyer of invaders and thus a deficiency would increase susceptibility to infections and perhaps even cancer. Cytotoxic T cells works in the same manner but are more likely related to induced responses. Not all antigens are harmful to us and thus you need to be more specific in your question.