Atezolizumab, Guadecitabine, and CDX-1401 Vaccine in Treating Patients With Recurrent Ovarian, Fallopian Tube, or Primary Peritoneal Cancer

Inclusion Criteria:

* Women with epithelial ovarian, fallopian tube, or primary peritoneal carcinoma with platinum-resistant disease (defined as having relapsed within 6 months of last platinum-containing regimen because we would like to include both primary and secondary resistance); patients are allowed to have had more than 2 prior cytotoxic treatment regimens; all patients should have received standard of care agents, which confer clinical benefit
* Presence of biopsiable disease and patient able to undergo pre-treatment and on-treatment biopsy
* Tissue available from primary and/or recurrent disease to evaluate tumor expression of NY-ESO-1 or PDL1 by immunohistochemistry (IHC) and/or reverse transcriptase-polymerase chain reaction (RT-PCR), and for measurement of DNA methylation
* No requirement for tumor expression of NY-ESO-1
* Life expectancy \> 6 months as assessed by study physician
* Because no dosing or adverse event data are currently available on the use of atezolizumab in combination with SGI-110 and CDX-1401 in patients \< 18 years of age, children are excluded from this study, but may be eligible for future pediatric trials
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2
* Have been informed of other treatment options
* Have measurable disease outside of biopsy site present per immune related (ir)RECIST criteria; (Rationale: Biopsy may also induce an inflammatory response and bias outcome measurements)
* Patients may have received previous NY ESO 1 vaccine therapy; patients who received bevacizumab or other experimental therapies are eligible for enrollment provided they have discontinued therapy (at least 4 weeks) prior to randomization and recovered from toxicities to less than grade 2
* Leukocytes \>= 2,500/mcL
* Absolute neutrophil count \>= 1,500/mcL
* Platelets \>= 100,000/mcL
* Hemoglobin \>= 10 g/dL
* Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) (however, patients with known Gilbert disease who have serum bilirubin level =\< 3 x ULN may be enrolled)
* Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 1.5 x ULN (AST and/or ALT =\< 3 x ULN for patients with liver involvement)
* Alkaline phosphatase =\< 2 x ULN (=\< 5 x ULN for patients with documented liver involvement or bone metastases)
* Creatinine clearance \>= 30 mL/min/1.73 m\^2 by Cockcroft-Gault
* International normalized ratio (INR) and activated partial thromboplastin time (aPTT) =\< 1.5 x ULN
* Administration of the drugs used in this study may have an adverse effect on pregnancy and poses a risk to the human fetus, including embryo-lethality; women of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 5 months (150 days) after the last dose of study agent; 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

Exclusion Criteria:

* Patients with prior allogeneic bone marrow transplantation or prior solid organ transplantation
* Patients who have had chemotherapy or radiotherapy including complementary and alternative medicine treatments (CAMs) within 4 weeks prior to entering the study or those who have not recovered from adverse events (other than alopecia) due to agents administered more than 4 weeks earlier
* Prior treatment with anti-PD-1, or anti-PD-L1 therapeutic antibody or pathway-targeting agents

  * Patients who have received prior treatment with anti-CTLA-4 may be enrolled, provided the following requirements are met:

    * Minimum of 12 weeks from the first dose of anti-CTLA-4 and \> 6 weeks from the last dose
    * No history of severe immune-related adverse effects from anti-CTLA-4 (NCI CTCAE grade 3 and 4)
* Treatment with any other investigational agent within 4 weeks prior to cycle 1, day 1
* Treatment with systemic immunostimulatory agents (including, but not limited to, interferon \[IFN\]-alpha or interleukin \[IL\]-2) within 6 weeks prior to cycle 1, day 1
* Treatment with systemic immunosuppressive medications (including, but not limited to, prednisone, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor necrosis factor \[anti-TNF\] agents) within 2 weeks prior to cycle 1, day 1

  * Patients who have received acute, low dose, systemic immunosuppressant medications (e.g., a one-time dose of dexamethasone for nausea) may be enrolled
  * The use of inhaled corticosteroids and mineralocorticoids (e.g., fludrocortisone) for patients with orthostatic hypotension or adrenocortical insufficiency is allowed
* Patients taking bisphosphonate therapy for symptomatic hypercalcemia; use of bisphosphonate therapy for other reasons (e.g., bone metastasis or osteoporosis) is allowed
* Concomitant systemic treatment with chronic use of anti-histamine or non-steroidal anti-inflammatory drugs and other platelet inhibitory agents and patients on oral anticoagulant (e.g. warfarin); exception: patients on therapeutic anticoagulation therapy such as low-molecular-weight heparin or warfarin at a stable dose level are allowed on study
* Patients with known primary central nervous system (CNS) malignancy or symptomatic CNS metastases are excluded
* Known hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies
* History of severe allergic, anaphylactic, or other hypersensitivity reactions to chimeric or humanized antibodies or fusion proteins
* History of allergic reactions attributed to compounds of similar chemical or biological composition to other agents used in this study
* Subjects who have received prior therapy with hypomethylating agents (5-azacytidine, decitabine, SGI-110)
* Mental impairment that may compromise the ability to give informed consent and comply with the requirements of the study
* Lack of ability of a patient for immunological and clinical follow-up assessment
* Evidence of current drug or alcohol abuse or psychiatric impairment, which in the investigator's opinion will prevent completion of protocol therapy or follow-up
* Due to unknown effects on the developing fetus or newborn, pregnant or nursing female patients are excluded from this study
* Unwilling or unable to follow protocol requirements
* Any condition which in the investigator's opinion deems the participant an unsuitable candidate to receive study drug. (i.e., any significant medical illness or abnormal laboratory finding that would increase the patient's risk by participating in this study)
* Known clinically significant liver disease, including active viral, alcoholic, or other hepatitis; cirrhosis; fatty liver; and inherited liver disease

  * Patients with past or resolved hepatitis B infection (defined as having a negative hepatitis B surface antigen \[HBsAg\] test and a positive anti-HBc \[antibody to hepatitis B core antigen\] antibody test) are eligible
  * Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA)
* History or risk of autoimmune disease, including, but not limited to, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener's granulomatosis, Sjogren's syndrome, Bell's palsy, Guillain-Barre syndrome, multiple sclerosis, autoimmune thyroid disease, vasculitis, or glomerulonephritis

  * Patients with a history of autoimmune hypothyroidism on a stable dose of thyroid replacement hormone may be eligible
  * Patients with controlled Type 1 diabetes mellitus on a stable insulin regimen may be eligible
  * Patients with eczema, psoriasis, lichen simplex chronicus of vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis would be excluded) are permitted provided that they meet the following conditions:

    * Patients with psoriasis must have a baseline ophthalmologic exam to rule out ocular manifestations
    * Rash must cover less than 10% of body surface area (BSA)
    * Disease is well controlled at baseline and only requiring low potency topical steroids (e.g., hydrocortisone 2.5%, hydrocortisone butyrate 0.1%, fluocinolone 0.01%, desonide 0.05%, alclometasone dipropionate 0.05%)
    * No acute exacerbations of underlying condition within the last 12 months (not requiring psoralen plus ultraviolet A radiation \[PUVA\], methotrexate, retinoids, biologic agents, oral calcineurin inhibitors; high potency or oral steroids)
* History of idiopathic pulmonary fibrosis, pneumonitis (including drug induced), organizing pneumonia (i.e., bronchiolitis obliterans, cryptogenic organizing pneumonia, etc.), or evidence of active pneumonitis on screening chest computed tomography (CT) scan; history of radiation pneumonitis in the radiation field (fibrosis) is permitted
* Patients with active tuberculosis (TB) are excluded
* Severe infections within 4 weeks prior to cycle 1, day 1, including, but not limited to, hospitalization for complications of infection, bacteremia, or severe pneumonia
* Signs or symptoms of infection within 2 weeks prior to cycle 1, day 1
* Received oral or intravenous (IV) antibiotics within 2 weeks prior to cycle 1, day 1; patients receiving prophylactic antibiotics (e.g., for prevention of a urinary tract infection or chronic obstructive pulmonary disease) are eligible
* Major surgical procedure within 28 days prior to cycle 1, day 1 or anticipation of need for a major surgical procedure during the course of the study
* Administration of a live, attenuated vaccine within 4 weeks before cycle 1, day 1 or anticipation that such a live, attenuated vaccine will be required during the study and up to 5 months after the last dose of atezolizumab

  * Influenza vaccination should be given during influenza season only (approximately October to March); patients must not receive live, attenuated influenza vaccine within 4 weeks prior to cycle 1, day 1 or at any time during the study and until 5 months after the last dose of atezolizumab
* 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
* Patients positive for human immunodeficiency virus (HIV) are NOT excluded from this study, but HIV-positive patients must have:

  * A stable regimen of highly active anti-retroviral therapy (HAART)
  * No requirement for concurrent antibiotics or antifungal agents for the prevention of opportunistic infections
  * A CD4 count above 250 cells/mcL and an undetectable HIV viral load on standard PCR-based tests
* Patients requiring treatment with a RANKL inhibitor (e.g. denosumab) who cannot discontinue it before treatment with atezolizumab