IL-15 Superagonist With or Without Vaccine in Biochemically Recurrent Prostate Cancer After Previous Stereotactic Body Radiation Therapy

Background: Biochemically recurrent prostate cancer (BCR) occurs when prostate-specific antigen (PSA) levels in the blood rise after surgery or radiation. BCR affects 30,000 to 50,000 men each year. Researchers want to know if a drug (N-803) alone or combined with a vaccine (ETBX-071) can reduce PSA in BCR prostate cancer after radiation. Objective: To test a study drug alone and combined with a vaccine in people with BCR prostate cancer who have been treated with targeted radiation to areas of recurrent prostate cancer in the past. Eligibility: People aged 18 years and older with BCR prostate cancer who have previously undergone treatment with stereotactic body radiation therapy (SBRT). Design: Participants will be screened. They will have a physical exam with blood tests. They will have tests of their heart and kidney function. They will have 3 different imaging scans of their tumors. N-803 is injected under the skin of the abdomen. ETBX-071 is injected under the skin of thigh. Participants will be divided into 2 groups: 1 group will get N-803 alone; 1 group will get both N-803 and ETBX-071. The drug or drugs will be given on the first day of 21-day treatment cycles. Participants will have 8 treatment cycles. Participants will have a follow-up visit 3 weeks after their last dose of the study drugs. Blood tests and all 3 imaging scans will be repeated. Follow-up visits will continue every 4 to 8 weeks for 5 years. These visits will include a positron emission tomography (PET) scan every 6 months.

* INCLUSION CRITERIA: * Histopathological confirmation of prostate adenocarcinoma by the Laboratory of Pathology at the National Institutes of Health (NIH) Clinical Center prior to the study treatment initiation. If no pathologic specimen is available, participants may enroll with a pathologist s report showing a histologic diagnosis of prostate adenocarcinoma and a clinical course consistent with the disease from any outside site. * Biochemically recurrent prostate cancer, defined as PSA over 0.8 ng/ml following radical prostatectomy or \>= 2 ng/ml above the nadir following definitive radiotherapy or definitive radiotherapy (including brachytherapy) for localized prostate cancer. * Participants must be at least 1 year removed from definitive local therapy before the study treatment initiation. * Recovery to baseline from acute toxicity related to prior therapy, including surgery and radiation. * Hepatic function eligibility parameters: Bilirubin (total and direct) \= 1000/mm\^3 * Platelet count \>= 100000/mm\^3 * Hemoglobin (Hgb) \>= 10 g/dL * Participants must be able to understand and willing to sign a written informed consent document. EXCLUSION CRITERIA: * Immunocompromised status due to: * Human immunodeficiency virus (HIV) seropositivity * HBV or HCV seropositivity * Other immunodeficiency diseases * Active autoimmune diseases such as Addison's disease, Hashimoto's thyroiditis, systemic lupus erythematosus, Sjogren syndrome, scleroderma, myasthenia gravis, Goodpasture syndrome or active Grave's disease. Participants with a history of autoimmunity that has not required systemic immunosuppressive therapy or does not threaten vital organ function including central nervous system (CNS), heart, lungs, kidneys, skin, and gastrointestinal (GI) tract will be allowed. Participants with diabetes type I, vitiligo, or alopecia are allowed. * Receipt of any organ transplantation, including allogeneic stem-cell transplantation, but with the exception of transplants that do not require immunosuppression (e.g., corneal transplant, hair transplant). * Chronic administration (defined as daily or every other day for continued use \> 14 days) of systemic corticosteroids within 28 days before the study treatment initiation. Note: Use of corticosteroids with minimal systemic absorption (e.g., inhaled steroids, nasal sprays, and topical agents) is allowed. * Other medications used for urinary symptoms including 5-alpha reductase inhibitors (finasteride and dutasteride) and alternative medications known to alter PSA (e.g., phytoestrogens and saw palmetto) within 28 days prior to the study treatment initiation. * Major surgery within 28 days prior to study treatment initiation. * Systemic therapy, including any investigational therapy within 28 days prior to the study treatment initiation. * Radiation therapy within 14 days prior to the study treatment initiation. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to the study drugs. * Clinically significant cardiovascular/cerebrovascular disease as follows: cerebral vascular accident/stroke (\< 6 months prior to the first planned dose of study drugs), myocardial infarction (\< 6 months prior to the first planned dose of study drugs), or any of the following at time of enrollment: unstable angina, congestive heart failure (New York Heart Association Classification Class \>= II), serious cardiac arrhythmia, or uncontrolled hypertension (SBP\>170/ DBP\>105). * Serious intercurrent medical illness evaluated by medical history and physical exam that would interfere with participant's ability to carry out the treatment program.