P53MVA and Pembrolizumab in Treating Patients With Recurrent Ovarian, Primary Peritoneal, or Fallopian Tube Cancer

Inclusion Criteria: * Participants with histologically or cytologically confirmed diagnosis of epithelial ovarian, primary peritoneal or fallopian tube cancer will be enrolled in this study; patients must have experienced recurrence or progression within 6 months after completion of platinum based chemotherapy (by Response Evaluation Criteria in Solid Tumors \[RECIST\] 1.1 criteria). * A patient is eligible to participate if she is not pregnant, not breast-feeding, and at least one of the following conditions applies: a.) Not a woman of childbearing potential (WOCBP) OR b.) A WOCBP who agrees to follow the contraceptive guidance during the treatment period and for at least 30 days after the last dose of study treatment * The participant (or legally acceptable representative if applicable) provides written informed consent for the trial * Have measurable disease based on RECIST 1.1., or detectable disease; lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions * 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 computed 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 patients is defined as one who does not have measurable disease, but has at least one of the following conditions: * Baseline values of 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 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 or refractory disease; these patients are not considered to benefit from additional platinum-based therapy and are treated with other sequential single agents; 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 will not be eligible for this trial * 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, since they have a favorable (33-59%) chance of responding to further rounds of platinum based chemotherapy * Patients with confirmed p53 mutation by molecular analysis and/or evidence of p53 overexpression by immunohistochemistry (\>= 10% of cells within tumor staining positive) will be eligible; this will be assessed semi-quantitatively by a Clinical Laboratory Improvement Act (CLIA) approved pathology core pathologist, using CLIA approved mutational analysis or immuno-histochemistry techniques on formalin-fixed paraffin-embedded tissue; in the case of equivocal immunohistochemistry (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; patients are not required to have PD-L1 positive ovarian tumors and PD-L1 testing is not mandatory on this study; however, we will collect the data on PD-L1 testing when available * Have an Eastern Cooperative Oncology Group (ECOG) performance status of =\< 2 (Karnofsky \>= 60%) and a life expectancy of at least 3 months * Up to 4 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; eligible Patients are those with documented disease recurrence/progression within 0-6 months of completing platinum-based chemotherapy; patients should not have received any non-oncology, viral vaccines within 30 days prior to starting protocol treatment * Absolute neutrophil count (ANC) \>= 1500/uL (collected within 14 days prior to the start of study treatment) * Platelets \>= 100 000/uL (collected within 14 days prior to the start of study treatment) * Hemoglobin \>= 9.0 g/dL or \>= 5.6 mmol/L (collected within 14 days prior to the start of study treatment) * Criteria must be met without erythropoietin dependency and without packed red blood cell (pRBC) transfusion within last 2 weeks * Creatinine =\< 1.5 x upper limit of normal (ULN) OR measured or calculated creatinine clearance (glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance \[CrCl\]) \>= 50 mL/min for participant with creatinine levels \> 1.5 x institutional ULN (collected within 14 days prior to the start of study treatment) * Creatinine clearance (CrCl) should be calculated per institutional standard * Total bilirubin =\< 1.5 x ULN OR direct bilirubin =\< ULN for participants with total bilirubin levels \> 1.5 x ULN (collected within 14 days prior to the start of study treatment) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) =\< 2.5 x ULN (=\< 5 x ULN for participants with liver metastases) (collected within 14 days prior to the start of study treatment) * International normalized ratio (INR) OR prothrombin time (PT) =\< 1.5 x ULN unless participant is receiving anticoagulant therapy as long as PT or activated partial thromboplastin time (aPTT) is within therapeutic range of intended use of anticoagulants (collected within 14 days prior to the start of study treatment) * Activated partial thromboplastin time (aPTT) =\< 1.5 x ULN unless participant is receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of intended use of anticoagulants (collected within 14 days prior to the start of study treatment) * Left ventricle ejection fraction (LVEF) \>= 55% (collected within 14 days prior to the start of study treatment) Exclusion Criteria: * A WOCBP who has a positive urine pregnancy test within 72 hours prior to study treatment start; if the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent or with an agent directed to another stimulatory or co-inhibitory T-cell receptor (eg, CTLA-4, OX-40, CD137) * Has received prior systemic anti-cancer therapy including investigational agents within 4 weeks prior to treatment start * Note: participants must have recovered from all adverse events (AEs) due to previous therapies to =\< grade 1 or baseline; participants with =\< grade 2 neuropathy may be eligible * Note: if participant received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting study treatment * Has received prior radiotherapy within 3 weeks of start of study treatment; participants must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis; a 1-week washout is permitted for palliative radiation (=\< 2 weeks of radiotherapy) to non-central nervous system (CNS) disease * Has received a live vaccine within 30 days prior to the first dose of study drug; examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guerin (BCG), and typhoid vaccine; seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (eg, FluMist) are live attenuated vaccines and are not allowed * Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks prior to the first dose of study treatment; Note: participants who have entered the follow-up phase of an investigational study may participate as long as it has been 4 weeks after the last dose of the previous investigational agent * Has a diagnosis of immunodeficiency (including organ grafts and human immunodeficiency virus \[HIV\]), or is receiving systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug (exceptions: nasal corticosteroids, inhaled steroids, adrenal replacement steroids and steroid creams are allowed) * Has a known additional malignancy that is progressing or has required active treatment within the past 3 years; Note: participants with basal cell carcinoma of the skin, squamous cell carcinoma of the skin, superficial bladder cancer or any carcinoma in situ (e.g. breast carcinoma, cervical cancer in situ) that have undergone potentially curative therapy are not excluded * Has known active CNS metastases and/or carcinomatous meningitis; participants with previously treated brain metastases may participate provided they are radiologically stable, i.e. without evidence of progression for at least 4 weeks by repeat imaging (note that the repeat imaging should be performed during study screening), clinically stable and without requirement of steroid treatment for at least 14 days prior to first dose of study treatment * Has severe hypersensitivity (\>= grade 3) to pembrolizumab and/or any of its excipients * Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs); replacement therapy (eg., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment * Has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis * Has an active infection requiring systemic therapy * Has a known history of human immunodeficiency virus (HIV) * Has active infection with hepatitis A (as determined by an acute hepatitis panel), a known history of hepatitis B (hepatitis B surface antigen \[Ag\] reactive), or active hepatitis C virus (qualitative hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] detectable) * Active TB (Bacillus tuberculosis) infection (as determined by Quantiferron Test) * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the subject's participation for the full duration of the study, or is not in the best interest of the subject to participate, in the opinion of the treating investigator * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial * Is pregnant or breastfeeding, or expecting to conceive children within the projected duration of the study, starting with the screening visit through 120 days after the last dose of trial treatment * Patients with a history of cardiac disease are excluded: myocardial infarction or arterial thromboembolic events within 6 months prior to baseline, severe or unstable angina, New York Heart Association Class III or IV disease, QTCB (corrected according to Bazett's formula) interval \> 470 msec, serious uncontrolled hypertension (systolic \> 150 and/or diastolic \> 100 mm Hg); baseline electrocardiography, echocardiography and assessment of serum troponin (I) are included in the screening exams; subjects in whom these assays are abnormal (electrocardiogram \[EKG\] excluding 1st degree branch block, sinus brachycardia, sinus tachycardia or non-specific T wave changes, serum troponin \>= grade 2) are ineligible * Patients with a family history or Li-Fraumeni syndrome will not be eligible * History of severe environmental allergies or allergy to egg proteins