p53MVA Vaccine and Gemcitabine Hydrochloride in Treating Patients With Recurrent Ovarian Epithelial Cancer

Inclusion Criteria: * Patients with histologically or cytologically confirmed, epithelial ovarian, primary peritoneal or fallopian tube cancer who experienced recurrence or progression within 12 months after completion of platinum based chemotherapy; patients must have measurable disease or detectable disease: * Measurable disease is defined as at least one lesion that can be accurately measured in at least one dimension (longest dimension to be recorded); each lesion must be greater than or equal to 10 mm when measured by computerized tomography (CT), positron emission tomography (PET)/CT or magnetic resonance imaging (MRI); lymph nodes must be greater than or equal to 15 mm in short axis when measured by CT, PET/CT or MRI * Detectable disease in a patient is defined as one who does not have measurable disease, but has at least one of the following conditions: * Baseline values of cancer antigen-125 (CA-125) at least 2 x upper limit of normal (ULN) * Ascites and/or pleural effusion attributed to tumor * Solid and/or cystic abnormalities on radiographic imaging that do not meet modified Response Evaluation Criteria In Solid Tumors (RECIST) criteria, immune-related response criteria (irRC) for target lesions * Patients whose ovarian cancer recurs/progresses within 0-6 months following platinum-based chemotherapy have platinum resistant disease; such patients are eligible for this trial * Patients with documented disease recurrence/progression within 6-12 months of completing platinum-based therapy, are considered to have 'borderline' platinum sensitivity; these patients are eligible for this trial if agreed by the patient and the treating physician * Patients who relapse more than 12 months after completion of platinum-based treatment are considered 'platinum sensitive' and will not be eligible for this trial * Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Patients must have a life expectancy of at least 3 months * Absolute neutrophil count \>= 1,500/ul * Platelets \>= 100,000/ul; low platelet counts may be corrected with transfusion to achieve eligibility for study * The hemoglobin level must be greater than 9 g/dL; low hemoglobin counts may be corrected with transfusion to achieve eligibility for study * Calculated or measured creatinine clearance \>= 50 ml/min or serum creatinine =\< 1.6 mg/dl * Total bilirubin =\< 1.5 x institutional upper limit of normal * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 3 times institutional upper normal level (AST and ALT =\< 5 times institutional upper normal level, if there is evidence of liver metastasis) * Women of childbearing potential must agree to use adequate contraception (hormonal or barrier method of birth control or abstinence) prior to study entry and for six months following duration of study participation; should a woman become pregnant or suspect that she is pregnant while participating on the trial, she should inform her treating physician immediately * Patients with confirmed p53 mutation by molecular analysis and/or evidence of p53 overexpression by immunohistochemistry (IHC) (\>= 10% of cells within the tumor staining positive) will be eligible; this will be assessed semi-quantitatively by a Clinical Laboratory Improvement Amendments (CLIA) approved pathology core pathologist, using CLIA approved mutational analysis or immunohistochemistry techniques on formalin-fixed paraffin-embedded tissue; in the case of equivocal IHC results, p53 involvement may be confirmed by detection of p53 molecular analysis on tumor deoxyribonucleic acid (DNA); patients on whom molecular analysis of p53 mutations is already available, will not require IHC analysis; molecular analysis may be performed as an additional research procedure at the end of the study (distinct from eligibility determination) if the principal investigator (PI) deems it of scientific value and research funding is available to cover the cost * All subjects must have the ability to understand and the willingness to sign a written informed consent * Up to 2 prior chemotherapy regimens for recurrent disease are allowed; adjuvant chemotherapy and maintenance Taxol after completion of six cycles of adjuvant carboplatin * Taxol will not be counted as a "prior chemotherapy regimen" for the purpose of this study; treatment with targeted agents or hormones would not be considered as a systemic chemotherapy regimen; previous treatment with gemcitabine is not allowable * Eligible patients are those with documented disease recurrence/progression within 0-12 months of completing platinum-based chemotherapy Exclusion Criteria: * Patients should not have any uncontrolled illness including 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 * No other malignancy is allowed except for the following: adequately treated basal or squamous cell carcinoma, superficial bladder cancer, any carcinoma in situ or any other cancer from which the patient has been disease free for at least 3 years * Patients may not be receiving any additional investigational agents or radiation therapy * History of severe environmental allergies or allergy to egg proteins * Pregnant women are excluded from this study * Patients with known brain metastases will be excluded * Patients who have had radiotherapy within 4 weeks prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier * Patients with a family history or Li-Fraumeni syndrome will not be eligible * Concurrent use of corticosteroids (exceptions: nasal corticosteroids, inhaled steroids, adrenal replacement steroids and steroid creams are allowed) * Patients with a history of immunodeficiency, including organ grafts and human immunodeficiency virus (HIV), will not be eligible * Subjects, who in the opinion of the investigator, may not be able to comply with the safety monitoring requirements of the study * Patients with any active autoimmune disease or a condition that requires systemic corticosteroids or other immunosuppressive medications will be excluded; exceptions to this are subjects with vitiligo, type I diabetes mellitus and autoimmune thyroiditis only requiring hormone replacement, who will be permitted to enroll