Sirolimus and Vaccine Therapy in Treating Patients With Stage II-IV Ovarian, Fallopian Tube, or Primary Peritoneal Cancer

Inclusion Criteria: * Women with stages II-IV epithelial ovarian, fallopian tube, or primary peritoneal carcinoma who have completed standard therapy for primary or recurrent disease (i.e., patients who would normally be observed); eligible patients may have asymptomatic residual measurable disease on physical examination and/or computed tomography (CT) scan, and/or may have an elevated cancer antigen 125 (CA-125); or may be in complete clinical remission after treatment for primary or recurrent disease; these patients would normally enter a period of observation after standard management * Any human leukocyte antigen (HLA) type (historic HLA typing is permitted) * Tumor expression of NY-ESO-1 by immunohistochemistry (IHC) and/or real-time polymerase chain reaction (RTPCR) * No history of previous severe allergic reactions to vaccines or unknown allergens * Life expectancy \> 6 months * Have an Eastern Cooperative Oncology Group (ECOG) performance status of =\< 2 * Hematology and biochemistry laboratory results within the limits normally expected for the patient population, without evidence of major organ failure * Absolute neutrophil count (ANC) \>= 1,000/uL * Platelets (PLT) \>= 75,000/uL * Hemoglobin (Hgb) \>= 8 g/dL * Total bilirubin =\< 1.5 x upper limits of normal (ULN) * Serum glutamic-oxaloacetic transaminase(SGOT)/aspartate aminotransferase (AST) or serum glutamate pyruvate transaminase(SGPT)/alanine aminotransferase (ALT) =\< 3 x ULN * Serum creatinine =\< 2 x ULN * Prothrombin time(PT)/international normalized ratio(INR) =\< 1.5 * Electrocardiogram, showing no indications of cardiac problems like congestive heart failure, myocardial infarction, and cardiomyopathy * Have been informed of other treatment options * Ability to swallow and retain oral medication * Participants of child-bearing potential must agree to use adequate contraceptive methods (e.g., hormonal or barrier method of birth control) prior to study entry; should a woman become pregnant or suspect she is pregnant while she is participating in this study, she should inform her treating physician immediately * Participant or legal representative must understand the investigational nature of this study and sign an Independent Ethics Committee/Institutional Review Board approved written informed consent form prior to receiving any study related procedure * Patients may have received previous NY-ESO-1 vaccine therapy Exclusion Criteria: * Metastatic disease to the central nervous system * Other serious illnesses (e.g., serious infections requiring antibiotics, bleeding disorders) * History of severe autoimmune disorders requiring use of steroids or other immunosuppressives * Concomitant systemic treatment with corticosteroids, anti-histamine or non-steroidal antiinflammatory drugs for \>2 weeks,, and other platelet inhibitory agents, strong inhibitors/inducers of cytochrome P450-3A4 (CYP450-3A4) * Chemotherapy, radiation therapy, or immunotherapy within 4 weeks prior to first dosing of study drug (6 weeks for nitrosoureas); concomitant hormonal therapies for breast cancers are allowed * Patients with a positive fecal occult blood test excluding hemorrhoids * Clinically significant heart disease (New York Heart Association \[NYHA\] class III or IV) within six months * Participation in any other clinical trial involving another investigational agent within 4 weeks prior to first dosing of study drug * Known hepatitis B, hepatitis C, or human immunodeficiency virus (HIV) * Mental impairment that may compromise the ability to give informed consent and comply with the requirements of the study * Lack of availability of a patient for immunological and clinical follow-up assessment * Known pulmonary hypertension * Known hypersensitivity to sirolimus * Evidence of current drug or alcohol abuse or psychiatric impairment, which in the Investigator's opinion will prevent completion of the protocol therapy or follow-up * Pregnant or nursing female patients * Unwilling or unable to follow protocol requirements * Any condition which in the investigator's opinion deems the patient an unsuitable candidate to receive study drug (i.e., any significant medical illness or abnormal laboratory finding that would, in the investigator's judgment, increase the subject's risk by participating in this study)