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

Inclusion Criteria:

* Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1
* Have measurable disease per RECIST 1.1 criteria present
* Participant may have serous, endometrioid, clear cell, mucinous or undifferentiated type of recurrent epithelial ovarian, fallopian tube, or primary peritoneal cancer

  * Histologic confirmation of the original primary tumor is required via the pathology report
* Participant can be either platinum-sensitive (platinum free interval \[PFI\] \>= 6 months prior to recent recurrence) or platinum-resistant (PFI \< 6 months prior to recent recurrence). If the participant has a platinum sensitive disease, she may only enroll in this clinical trial if there is a contraindication for her to receive further treatment with platinum-based chemotherapy (such as serious, persistent toxicity or sever hypersensitivity to platinum agents or she declines standard of care).
* Participant must be willing to undergo core or excisional biopsy of a tumor lesion within 4 weeks (28 days) prior to initiation of treatment on day 1 and after 3 cyles of study treatment; participants for whom newly obtained samples cannot be provided (e.g. inaccessible or subject safety concern) may submit an archived specimen only upon agreement from the principal investigator
* Absolute neutrophil count (ANC): \>= 1,500 /mcL
* Platelets: \>= 100,000 / mcL
* Hemoglobin: \>= 9 g/dL or 5.6 mmol/L without transfusion or erythropoietin (EPO) dependency (within 7 days of assessment)
* Serum creatinine: =\< 1.5 X upper limit of normal (ULN) OR measured or calculated creatinine clearance \>= 60 mL/min for participant with creatinine levels \> 1.5 X institutional ULN; glomerular filtration rate (GFR) can also be used in place of creatinine or creatinine clearance (CrCl)
* Urine protein creatine ratio (UPCR) \< 1 prior to enrollment
* Serum total bilirubin: =\< 1.5 X ULN OR direct bilirubin =\< ULN for participants with total bilirubin levels \> 1.5 ULN
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase\[SGOT\]) and alanine transaminase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]): =\< 2.5 X ULN OR =\< 5 X ULN for participants with liver metastases
* Albumin: \> 2.5 mg/dL
* International normalized ratio (INR) or prothrombin time (PT): =\< 1.5 unless participant is receiving anticoagulant therapy as long as PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants
* Activated partial thromboplastin time (aPTT): =\< 1.5 X ULN unless participant is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants
* Participants of childbearing potential must have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication; if the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required
* Participants of childbearing potential must be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication (participants of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year); 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 has recovered from toxicities of prior chemotherapy or other therapy (to grade 2 or less)
* Participant may have received prior investigational therapy (including immune therapy)
* Participant may have received prior hormonal therapy
* Participant may have received bevacizumab (or other antiangiogenic agent) and/or cyclophosphamide in the past
* Participant has had at least 4 weeks of postoperative recovery from surgery prior to enrollment to ensure complete wound healing; participants with bowel resections at surgery should begin protocol at least 42 days after surgery
* Ability to swallow and retain oral medication
* 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

Exclusion Criteria:

* Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 4 weeks of the first dose of treatment
* Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment or, is taking any other medication that might affect immune function
* Has a known history of active bacillus tuberculosis (TB)
* Hypersensitivity to bevacizumab, cyclophosphamide, pembrolizumab or any of its excipients
* Has had a prior anti-cancer monoclonal antibody (mAb) within 4 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier
* Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to a previously administered agent

  * Note: participants with =\< grade 2 neuropathy are an exception to this criterion and may qualify for the study
  * Note: if participant received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy and, has to be at least 28 days after the surgery
* Has a known additional malignancy that is progressing or requires active treatment: exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or cervical cancer in situ that has undergone potentially curative therapy
* Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis; participants with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to trial treatment; this exception does not include carcinomatous meningitis which is excluded regardless of clinical stability
* Has active autoimmune disease that has required systemic treatment in the past 6 months (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs); replacement therapy (e.g. thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment
* Has known history of, or any evidence of active, non-infectious pneumonitis
* Has an active infection requiring systemic therapy
* Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the participant's participation for the full duration of the trial, or is not in the best interest of the patient 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 within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment
* Has received prior therapy with an anti-PD-1, anti-programmed cell death 1 ligand 1 (PD-L1), or anti-programmed cell death 1 ligand 2 (PD-L2) agent
* Has a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies)
* Has known active hepatitis B (e.g., hepatitis B surface antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected)
* Has received a live vaccine within 30 days of planned start of study therapy

  * Note: seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., FluMist) are live attenuated vaccines, and are not allowed
* Active or history of inflammatory bowel disease (colitis, Crohn's), diverticulitis, irritable bowel disease, celiac disease, or other serious, chronic, gastrointestinal conditions associated with diarrhea; active or history of systemic lupus erythematosus or Wegener's granulomatosis
* Participant has clinical symptoms or signs of partial or complete gastrointestinal obstruction or, requires parenteral hydration and/or nutrition
* Participant requires, or is likely to require, more than a two-week course of corticosteroids for intercurrent illness; participant must complete the course of corticosteroids 2 weeks before screening to meet eligibility
* Participant has a serious, non-healing wound, ulcer, or bone fracture
* Participant has a clinically significant cardiovascular disease including:

  * Uncontrolled hypertension, defined as systolic \> 150 mmHg or diastolic \> 90 mmHg
  * Myocardial infarction or unstable angina within 6 months prior to enrollment
  * New York Heart Association (NYHA) grade II or greater congestive heart failure
  * Participant has a grade II or greater peripheral vascular disease
  * Participant has a clinically significant peripheral artery disease (e.g. those with claudication, within 6 months)
* Participant has organ allografts
* Participant is receiving medication(s) that might affect immune function
* Unwilling or unable to follow protocol requirements