AVB-S6-500 and Durvalumab in Treating Patients With Platinum-Resistant or Recurrent Ovarian, Fallopian Tube, or Primary Peritoneal Cancer

Inclusion Criteria: * Ability to provide signed informed consent * Patient is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations including follow up * Histology (reviewed at MD Anderson Cancer Center \[MDACC\]) showing recurrent high grade epithelial ovarian, peritoneal, or fallopian tube cancer * Platinum resistant or refractory disease as defined by progression of disease on a platinum-containing regimen or recurrence of disease within 180 days of previous platinum treatment * Have measurable disease based on modified RECIST 1.1. For the purposes of this study measurable disease is defined at least one "target lesion" that can be accurately measured in at least one dimension (longest dimension to be recorded). Each target lesion must be \> 20 mm when measured by conventional techniques, including palpation, plain x-ray, computed tomography (CT), and magnetic resonance imaging (MRI), or \> 10 mm when measured by spiral CT. The target lesion must be distinct from other tumor areas selected for pre-treatment biopsies. Pre-treatment imaging must be performed within 4 weeks of starting therapy * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Life expectancy of \>= 12 weeks * Body weight \> 30 kg. Note: if subject's weight falls below 30 kg during study but the patient is otherwise eligible to continue investigational therapy the dose of durvalumab will be modified to be weight-based (20 mg/kg for the 1500 mg dose; modification is not required for 1120 mg dose) * Hemoglobin \>= 9.0 g/dL * Absolute neutrophil count (ANC) \> 1500/mm\^3 * Platelet count \>= 100 x 10\^9/L (\> 75,000/mm\^3) * Serum bilirubin =\< 1.5 x upper limit of normal (ULN) * This will not apply to patients with confirmed Gilbert's syndrome (persistent or recurrent hyperbilirubinemia that is predominantly unconjugated in the absence of hemolysis or hepatic pathology), who will be allowed only in consultation with their physician * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamic-pyruvic transaminase \[SGPT\]) =\< 2.5 x ULN unless liver metastases are present, in which case it must be =\< 5 x ULN * Measured creatinine clearance (CL) \> 40 mL/min or calculated creatinine CL \> 40 mL/min by the Cockcroft-Gault formula (Cockcroft and Gault 1976) or by 24-hour urine collection for determination of creatinine clearance * Evidence of post-menopausal status or negative serum pregnancy test for female pre-menopausal patients. Women will be considered post-menopausal if they have been amenorrheic for 12 months without an alternative medical cause. The following age-specific requirements apply: * Women \< 50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of exogenous hormonal treatments and if they have luteinizing hormone and follicle-stimulating hormone levels in the post-menopausal range for the institution or underwent surgical sterilization (bilateral oophorectomy or hysterectomy) * Women \>= 50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of all exogenous hormonal treatments, had radiation-induced menopause with last menses \> 1 year ago, had chemotherapy-induced menopause with last menses \> 1 year ago, or underwent surgical sterilization (bilateral oophorectomy, bilateral salpingectomy or hysterectomy) * Patients must have no currently available standard of care treatment options Exclusion Criteria: * Participation in another clinical study with an investigational product (IP) during the last 28 days * Concurrent enrollment in another clinical study, unless it is an observational (non-interventional) clinical study or during the follow-up period of an interventional study * Receipt of the last dose of anticancer therapy (chemotherapy, immunotherapy, endocrine therapy, targeted therapy, biologic therapy, tumor embolization, monoclonal antibodies) =\< 28 days prior to the first dose of study drug. If sufficient wash-out time has not occurred due to the schedule or pharmacokinetic (PK) properties of an agent, a longer wash-out period will be required, as agreed by AstraZeneca, Aravive, and the investigator * Any unresolved toxicity National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) grade \>= 2 from previous anticancer therapy with the exception of alopecia, vitiligo, and the laboratory values defined in the inclusion criteria * Patients with grade \>= 2 neuropathy will be evaluated on a case-by-case basis after consultation with the primary investigator * Patients with irreversible toxicity not reasonably expected to be exacerbated by treatment with durvalumab may be included only after consultation with the study physician * Any concurrent chemotherapy, IP, biologic, or hormonal therapy for cancer treatment * Major surgical procedure (as defined by the investigator) within 28 days prior to the first dose of IP. Note: Local surgery of isolated lesions for palliative intent is acceptable * History of allogenic organ transplantation * Active or prior documented autoimmune or inflammatory disorders (including inflammatory bowel disease \[e.g., colitis or Crohn's disease\], diverticulitis \[with the exception of diverticulosis\], systemic lupus erythematosus, sarcoidosis syndrome, or Wegener syndrome \[granulomatosis with polyangiitis, Graves' disease, rheumatoid arthritis, hypophysitis, uveitis, etc\]). The following are exceptions to this criterion: * Patients with vitiligo or alopecia; * Patients with hypothyroidism (e.g., following Hashimoto syndrome) stable on hormone replacement; * Any chronic skin condition that does not require systemic therapy; * Patients without active disease in the last 5 years may be included but only after consultation with the primary investigator; * Patients with celiac disease controlled by diet alone * Uncontrolled intercurrent illness, including but not limited to, ongoing or active infection, symptomatic congestive heart failure, uncontrolled hypertension, unstable angina pectoris, cardiac arrhythmia, interstitial lung disease, serious chronic gastrointestinal conditions associated with diarrhea, or psychiatric illness/social situations that would limit compliance with study requirement, substantially increase risk of incurring Adverse Events (AEs) or compromise the ability of the patient to give written informed consent * Any medical, social, or psychological condition that would interfere with evaluation of study treatment or interpretation of patient safety or study results * Active infection including tuberculosis (clinical evaluation that includes clinical history, physical examination and radiographic findings, and tuberculosis \[TB\] testing in line with local practice), hepatitis B (known positive hepatitis B virus \[HBV\] surface antigen \[HBsAg\] result), hepatitis C, or human immunodeficiency virus (positive HIV 1/2 antibodies). Patients with a past or resolved HBV infection (defined as the presence of hepatitis B core antibody \[anti-HBc\] and absence of HBsAg) are eligible. Patients positive for hepatitis C (HCV) antibody are eligible only if polymerase chain reaction is negative for HCV ribonucleic acid (RNA) * History of another primary malignancy except for the following histories: * Malignancy treated with curative intent and with no known active disease \>= 5 years before the first dose of IP and of low potential risk for recurrence * Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease * Adequately treated carcinoma in situ without evidence of disease * History of leptomeningeal carcinomatosis * Brain metastases or spinal cord compression. Patients with suspected brain metastases at screening should have a magnetic resonance imaging (MRI) (preferred) or computed tomography (CT), each preferably with intravenous (IV) contrast of the brain prior to study entry * Mean QT interval corrected for heart rate using Fridericia's formula (QTcF) \>= 470 ms * Current or prior use of immunosuppressive medication within 14 days before the first dose of durvalumab or AVB-S6-500. The following are exceptions to this criterion: * Intranasal, inhaled, topical steroids, or local steroid injections (e.g., intra articular injection); * Systemic corticosteroids at physiologic doses not to exceed 10 mg/day of prednisone or its equivalent; * Steroids as premedication for hypersensitivity reactions (e.g., CT scan premedication) * Receipt of live attenuated vaccine within 30 days prior to the first dose of IP. Note: Patients, if enrolled, should not receive live vaccine whilst receiving IP and up to 90 days after the last dose of IP * Female patients who are pregnant or breastfeeding or of reproductive potential who are not willing to employ effective birth control from screening to 180 days after the last dose of durvalumab + AVB-S6-500 combination therapy * Known allergy or hypersensitivity to any of the study drugs or any of the study drug excipients * Unresolved partial or complete small or large bowel obstruction * Judgment by the investigator that the patient is unsuitable to participate in the study and the patient is unlikely to comply with study procedures, restrictions and requirements