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 modif…