All study candidates will be tested to see if their cancer has a p53 abnormality and if their immune system mounted a defense against it. These tests may include a tumor biopsy (removal of a small part of the tumor for microscopic examination); lymphapheresis (a procedure to take blood, remove white blood cells called lymphocytes, and return the red cells); and an immune response test similar to a skin test for tuberculosis. During the study, patients will have additional skin tests and blood tests.