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

Inclusion Criteria: * Clinically confirmed no evidence of disease \>= 90 days from completion of systemic therapy with the exception of hormonal therapy and bisphosphonates (per practice guidelines for breast and ovarian cancer) * Histological or cytological confirmation of stage II or III breast cancer or stage II, III, or IV ovarian/primary peritoneal/fallopian tube cancer; Note: patients with stage IV ovarian/primary peritoneal/fallopian tube cancer must register within one year of completing chemotherapy * Completed systemic treatment (chemotherapy, immune modulators \[such as trastuzumab\], radiation, and/or corticosteroids) with the exception of hormonal therapy and bisphosphonates \>= 90 days prior to registration * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0 or 1 * Absolute neutrophil count (ANC) \>= 1500/mm\^3 * Platelets \>= 100,000/ul * Hemoglobin \>= 10.0 g/dL * Creatinine =\< 1.5 x upper limit of normal (ULN) or 24 hour urine =\< grade 2 * Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) =\< 3 x ULN * Serum albumin \>= 3 g/dL * Urinalysis with =\< 2+ proteinuria * Thyroid-stimulating hormone (TSH) - negative or =\< normal institutional range * Anti-nuclear antibody (ANA) - negative or =\< normal institutional range * Serum rheumatoid factor (RF) - negative or =\< normal institutional range * Negative serum pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only * Capable of understanding the investigative nature, potential risks, and benefits of the study and capable of providing valid informed consent * Willing to return to Mayo Clinic Rochester for follow-ups (immunizations, blood draws, etc.) * Willing to provide mandatory blood samples for primary and correlative goals * Willing to receive a tetanus vaccination if you have not had one within the past year Exclusion Criteria: * Any of the following: * Pregnant women * Nursing women unwilling to stop breast feeding * Men or women of childbearing potential who are unwilling to employ adequate contraception from the time of registration through cycle 6 (or the final vaccine cycle for each patient) * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens * Immunocompromised patients (other than that related to the use of corticosteroids) including patients known to be human immunodeficiency virus (HIV) positive * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Receiving any other investigational agent * Other active malignancy =\< 5 years prior to registration; EXCEPTIONS: Non-melanoma skin cancer or carcinoma-in-situ of the cervix; NOTE: If there is a history of prior malignancy, they must not be receiving other specific treatment (cytotoxics, monoclonal antibodies, small molecule inhibitors) for this cancer * Known history of autoimmune disease * Any contraindication to receiving sargramostim (GM-CSF) or cyclophosphamide * Uncontrolled acute or chronic medical conditions including, but not limited to the following: * Active infection requiring antibiotics * Congestive heart failure (New York Heart Association class III or IV; moderate to severe objective evidence of cardiovascular disease) * Myocardial infarction or stroke within previous 6 months * Use of a systemic steroid =\< 30 days prior to registration * Receiving thyroid replacement therapy